The City is only 4 square miles and has quite a high living density with 48,000 residents (it also has 51 parks - some of which have long walking trails). the high density means that it has quite a few highrises, a lot within a block or two of the Lonsdale Corridor. It has a town centre (The Lonsdale Corridor and the Quay). The Canadians hereabouts think Lonsdale Avenue is very British in style, I can only assume it is due to having variety of stores along the main road (instead of popping them in malls). These days the area it is still lively after 9pm.
The District surrounds the City, is substantially larger in size, is more of a suburb and has a very low residence density with 83,000. It does not have a downtown core, but has four hubs, Edgemont Village, Lynn Valley, Parkgate and the lovely marina village of Deep Cove. According to McLeans magazine the District of North Vancouver was one of the 6 safest parts of Canada (2006).
Both the District and City are quite proud of their differences.
North Vancouver has beaches (well, actually the best are in West Vancouver, but that is not far to drive); forests (especially the Seymour Demonstration Forest); and three ski hills Cypress, Grouse and Seymour (which are all wonderful for summer walking hikes too). There are also 5 libraries, 4 swimming pools, 5 ice rinks (some are seasonal) and 8 (possibly more) community centres.
North Vancouver is built on the slopes of the local mountains. It does mean that it comes in for more than its fair share of rain and snow, especially in the higher elevations. Vancouver Precipitation will show you how wet it can be.
The City of North Vancouver has more jobs than residents (according to the 2001 census) but also is handy for commuting to Downtown Vancouver (accessible by a decent transit system and the wonderful SeaBus - a small commuter ferry that runs every 15 minutes during the peak hours).
From the District there is good access to the other cities is via the upper levels highway (The Trans Canada Highway 1). From a transportation point of view this is a downside to living on the North Shore - if the two bridges (Second Narrows and the Lions Gate Bridge) have accidents on them then you are cut off from anywhere except Squamish and Whistler.
The school district includes French Immersion (in six elementary schools and two high schools), one intermediate school, two alternate schools (with self learning programs) and seven high schools. There are moves to bring in International Baccalaureate programs. Additionally there are three Roman Catholic elementary schools, (St Edmunds, Holy Trinity and Pius XI) and one high school (St Thomas Aquinas). (NOTE: in BC religious schools are fee paying). There are also some private schools, eg Waldorf, Collingwood, Mulgrave, Bodwell.
North Vancouver, British Columbia - Detailed City Profile - A good source of information for North Vancouver (weather, demographics, employments, etc.)