Yes, Crystal Beach is a large vacation community that has lots of American owners. When I went through last summer it seemed like at least half the houses had NY plates parked out front. Crystal Beach is probably the nicest single beach on all of Lake Erie, so it's a very popular vacation spot.
The Lake Erie "cottages" are often more like small houses in beach towns though and rarely have direct lake frontages which is the typical "cottage" definition in the Toronto area.
When I think of cottage, I think of the thousands of lakes north of Toronto line with well treed, large private lots with small to massive vacation dwellings on them. Something like this:
https://kennisiscottagerentals.com/cleary-cottage/
A more typical Lake Erie "cottage" is more like a small dwelling on a quiet little street within a few minutes walk of a public beach, like these ones in Turkey Point, ON:
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To me these are more beach houses than cottages, more like something you would see lining the US east coast in the hundreds of little beach towns.
The north shore of Lake Erie is lined with little beach communities like this. The north side of the lake is generally cleaner and while the water can still be somewhat murky, the lake's shallow depth and southern location means it has a fairly lengthy swimming season compared to the other great lakes which are often consistently cold for the entire summer.
I swim in both Erie and Ontario every summer and Ontario is definitely "nicer" water, but the beaches are more limited in size, location, and niceness, and the water is consistantly cold other than maybe in late August in an unusually hot summer. Lake Erie comparatively has a solid 3 months of warm water and much nicer beaches.