There are things you know about your home town that you don't even know that you know. For example, I was born and grew up in Greater Vancouver, and I instinctively understand the bizarro terminology for parts of the city that must seem simply insane to anyone just arriving here.
Here's what I mean. East Vancouver, the East End, and the East Side are all the same thing—essentially the entire portion of the City of Vancouver east of Quebec Street (or, depending on where you are and how you define it, maybe Cambie Street or Main Street, which are both close by). Cool, fine, makes sense.
However, West Vancouver, the West End, and the West Side all represent completely different places. West Vancouver is actually a different city (Canada's richest, by the way), across Burrard Inlet northwest of Vancouver proper. The West End is part of the City of Vancouver, but a tiny part, the dense residential area of the downtown peninsula northwest of Burrard Street and southeast of Stanley Park (and not usually including stuff north of Georgia Street near Coal Harbour).
The West Side is different again, basically the converse of the East Side (or East End, or East Van)—the large swath of the city west of Quebec Street (or Cambie, or Main), extending out to Point Grey and the ocean. The Downtown East Side (or Downtown Eastside, one word) is the opposite (in many ways) of the West End and the West Side and West Vancouver. It is on the opposite side of downtown from the West End, and is Canada's poorest neighbourhood. In a sane world, it would be the East End compared to the West End, or alternatively the West End would be the Downtown Westside. But no.
Then we get to north and south. North Vancouver is again a different city (actually two—a City and a District—and no, I don't understand that either), again across Burrard Inlet, next to West Vancouver. Yes, West Vancouver and North Vancouver are next to each other, west to east, with neither one further north or south than the other, and together they constitute (get this) the North Shore.
(By the way, those of you used to the North Shore being on Oahu in Hawaii will be even further confused. In Hawaii, the North Shore means the northernmost land area of the island of Oahu, facing north. It is, in other words, the shore on the north side of the island, and is part of Oahu. In Vancouver, the North Shore is the southernmost land area to the north of the city itself, facing south across the inlet. It is the shore on the north side of the water, and is not part of Vancouver itself—even when we call it Vancouver's North Shore.)
South Vancouver encompasses parts of both the West Side and the East Side/East Van/East End. The southern parts, quite logically. Sometimes you also hear South Slope, or rarely the South Side, since most of that region slopes down from the high ground running east to west across the city. No one ever calls it the South End, and there is no North End or North Side either. There is also no South Shore.
There is a formal definition for Greater Vancouver (a.k.a. Metro Vancouver), encompassing suburban municipalities around, and mostly east of, the City of Vancouver, and which pay certain taxes to the Metro Vancouver district government (formerly the Greater Vancouver Regional District). But many locals extend that definition to reach out into the Fraser Valley to the east, and sometimes up Howe Sound to Squamish in the north these days. The boundaries expand as people commute farther and farther.
Finally, one more thing about the east-west dichotomy. Traditionally, Vancouver's East Side has been working class and the West Side more upper class, in broad terms. But these days, no one with a single (or double) working-class income could afford a new house anywhere in the City of Vancouver, because it's easy to find single-family detached homes approaching a million dollars, even in the most distant corners of East Van. That's what those expanding commuter boundaries are all about. Without help from family, existing real estate, or obscenely high incomes, first-time home buyers wanting to live in Vancouver itself are looking at a condominium or townhouse (and possibly an older one) at best.
In part because of that, the City of Surrey, part of Metro Vancouver, will likely exceed Vancouver's population in the next decade or so, and already covers a much larger area, but we won't be calling this place Metro Surrey anytime soon.