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I mean it pretty literally, i.e., the first reaction when someone looks at them (especially if that someone isn't a mathematician) should be "okay, these are definitely totally different things".
Maybe #3 and #4 are in conflict, mostly #4 is just more important. Like, any continuous function is probably good enough, and there have to be some more "different" looking continuous deformations than what I can think of. (Doesn't have to be topological spaces, but that would be one approach.)