Air Canada is part of the Star Alliance, as far as I know.

I was looking to book flights, from Europe to Toronto, any which way, cheapest choice would be the choice.

What I've noticed is that the same flight or flights ( code share ) are considerably cheaper on another airline, namely Lufthansa.

So the first flight is with a Lufthansa flight to a German airport, to change on an Air Canada flight ( but a Lufthansa flight number and a code share ) to Canada. ( And the transatlatic flight is really an Air Canada operated flight, just with several flight numbers )
The price tag is nearly half of what Air Canada would be charging for the same flight.

Is this usual?

What is "usual" in today's crazy-insane-mad-loony-whacko air travel industry??

As a regular traveler around Southeast Asia, I fairly haunt the web sites in search of the best airfares. Like you, I've found many discrepancies in prices for what I easily identify as the same flight.

I tend to use the comparison sites and then go to the airline site to see if the fares are better. Some third party web sites offer better deals, others don't.

Then there's the baggage scam. In Indonesia, third party sites often try to sell discounted (by only a dollar or two) airfares without baggage, for which they ask an extra payment. I then check the airline site and find the baggage is included in the fare for the same flight. Or the opposite.

For me, if I'm looking for a fare to somewhere, my bottom line is to go with the cheapest version of the same flight. Altho' I have to say I nowadays prefer to book directly with the airline and not a third party site, for the main reason that if I have to cancel or the airline cancels my flight, the third party site often as not will take a commission to rebook the flight. The airline won't.

In flying as in all else in real world life, the KISS principle should prevail...

I am aware of the baggage scam these days. Comparison sites rarely show the suticase, some do, some don't. Most likely the suitcase isn't included in the price.

Today one would have to add a whopping extra 200 Euros for a return flight from mainland Europe to Canada if a suitcase is checked. Carry on still seems to be for free as long as dimensions and weight limits are observed.

Air Canada is getting a bit ridiculous lately, excessive charges for checked suitcases as well as seat reservations. KLM is far more competitive in these matters, and surprisingly Lufthansa as well.

Flights via the US to Canada also seem cheaper, but it comes at the cost of having to queue at US immigration, long wait times and ridiculous questions by immigration officers about entering a country one is only transiting through to get to Canada.

There are simply more flights to the US, than to Canada, hence bigger competition and better price.

Incidentally Air Canada seems rather liberal on weight of checked luggage. At YYZ they don't seem to weigh checked suitcases. I knew I was once at 24 kilos while 23 kilos is the limit. They didn't bother and that was as recent as April this year.

Doesn't answer the OPs point but maybe useful anyway -

if you go onto an airlines website to check prices, leave and then return, clear down your cookies before you return - otherwise the price you were originally quoted will rise!

Thanks. I am aware of this practice as well.

Using the TOR browser is one choice of starting one's search, same as the incognito window of the browser.

Oops, yes. I forgot this one. I've known (and practiced) this for a long time.

Traveloka seems the worst site for this, tho' other third party sites likely come close. Of late I've noted they are also seeking a 'convenience charge' of up to $10 on a flight booking. They pulled this stunt on me last month, when I went to finalize and pay for a flight from Surabaya to Kuala Lumpur. I won't be using them again, and I've let them know by email that I'm no longer playing along with this little scam. Oddly, no response from them so far...

The cheaper Asian airlines seem to change their price by the hour. Also a few months ago I was looking for my usual Indonesia-Malaysia flight and I wandered into the Super Air Jet site - this is a fairly new airline, another of the infamous Lion Air's offshoot of same but differently named buckets. The flight I was looking at (Surabaya-Penang) was $169. (The Penang flights are usually $75-$90 but this was for August, high season in SE Asia).

Anyway, I closed down the site and cleared my cookies. A few hours later I returned to it and lo, behold, I found the same flight for $144. Hoo, a $24 saving!! Closed down again, checked the next day, same tactic, the first time $159, two hours later $135. No humongous $$$ saving to crow about over those two days, but the price variations were notable.

BTW I was using different laptops on the two days. I've never figured out if this makes a difference. Maybe yes, maybe no. Anyway, all the cookies were cleared immediately after logging out of Traveloka.

In the end I booked my usual Surabaya-KL flight, but not with Super Air Jet. Those el cheapo airlines are apparently discounting heavily in Indonesia now to fill their planes, so the flights can be crowded and the passengers guest workers or first-time kampung flyers. So far nobody has tried to bring a live chicken on a flight, unlike on a Middle East flight I took in 1971. SAJ can be a flying circus at times, the decibels level can be ear-shattering.

In my old age I now book always directly with the airline, and I prefer to pay a little extra and fly with airlines that won't try to charge me for water.

I think Asia is also a very different airline market than Canada. Also Canada differs strongly from the US, in terms of price and competition.
The fundamental problem in Canada is lack of competition and vast distances. Thus price is always more an issue in Canada no matter what way you're looking at it.

And then the pandemic, the war in the Ukraine, interest rate hikes and the cost of living crises were added on top of everything.

It used to be, around 500 Euros return PLUS ( or included, for those who don't understand) checked suitecase and first come first serve seat free, seat reservation from Europe to Canada East, and around 700 Euros for the same Canada West coast. And that was during summer, not winter, spring or fall.

These were the good times. They won't come back, sadly.

Now they advertize an "awesomely cheap" price, but add 200 Euro return for a checked suitcase, and another 50 Euros for the seat reservation later on. Also these charges don't come up on comparison sites.

Yes, Asia is very different to Canada. As for Australia, we down here suffer from the same lack of competition, also control by the monopoly of this country's biggest airlines, as you Canadians seem to be facing there. Odd, this, to me, as after all Canada is the closest neighbor (overlooking Mexico) to the USA, where competition prevails and low prices were always the norm.

Covid undid a lot of low priced things everywhere. Air Asia, which I flew with often until the 2020 lockdowns, at which time AA 'froze' all its outstanding air tickets and then delayed and dithered and stalled over refunds - they still owe me $80 which I realize I will never ever get, but then I retaliate by refusing to ever fly with them again, as do many of my Indonesian friends who also lost money to the AA cash grab.

Please keep us posted on your online adventures in getting the best fare. This information will surely be valuable to many who intend to fly to Canada in the next, say, year. SO and I had plans to return to Canada (I left in 1974) next year, but so far my admittedly random forays into the internet world of travel has only confused me. Web sites post one price now and another different (and usually higher) price an hour later. Many third party sites seem to (are they doing it deliberately? one tends to think yes) either withhold details or make them so vague or difficult to find that most people trying to book will overlook things like baggage. Then there is the hidden Convenience Charge which can pop up when you go to finalize and pay. The logic behind this latter piece of shysterism is the party who has made it that far into the site and done all the detail work on a booking, will then think, "oh, well!" shrug their shoulders and cough up the extra $10, $15 or even $20. As many will, and the sites know this. (I don't, but that's just me.)

I have said this before and I will repeat it. Look up air fares on all the 3P sites an go with the best one. Book directly with the airline. As I think you wrote anyway, so well done, if. Don't forget the baggage!!

Nowadays I try to no longer fly with any bucket airline charging me for a basic seat or even water during the flight. But even here in Asia my options have narrowed a lot since the unlocking of Covid restrictions.

Also, book and fly with a reputable airline. You know which one they are. In Australia, we have so little damn choice in this area. Consider that the soon-to-be-retired CEO of Qantas, in his time as head honcho at that once-great airline, did no end of mischief to its prestige and reputation but will leave his office in October with AUD $9 MILLION in payout - at least this was reduced from his original bye-bye payment of AUD $20 million