Somebody mentioned the "Gatineau" totoo in a comment, that's really local to "the Ottawa Region". I've only day-tripped and skied there, so I'd try Google for that, Gatineau camping -- the Quebec web sites might display French-first but (if you don't read French) they most likely have an English version, see e.g. the top-right corner of this web page. I imagine that anything in the Gatineau is likely to be very popular (i.e. need booking in advance), perhaps more than Algonquin, so more regulated. I think it's run by the "National Capital Commission" which is maybe federal rather than provincial. I guess it will be pleasant unless you don't like neighbours or something, but not backcountry, I think you're meant to stay on the official trails there.
Actually I haven't seen Canadian forest or woods (or brush) that canyou could easily walk through except on a designated pre-prepared trail, (or in winter on skis if the snow is really deep) -- I don't know what it's like in Russia -- I think that in somewhere like Southern Ontario you're likely to be on a hiking trail or going by canoe (or kayak or whatever) and (if you're paddling) perhaps preferring to avoid paddling upstream by staying on lakes.
Yes I'd guess you can do that in a park (depending on how good the fishing is) -- except cutting firewood, though you can collect dead wood -- walking on a hiking trail and booking a camp-site.
Or a lot of backcountry campsites might be intended for access by canoe, not on a hiking trail but e.g. on an island in a lake -- islands are good camping-spots.