SSE3+ & AVX{,2,-512} & co improve on SSE in pretty much the same way that x86-64 improves on x86 - the old thing still works just fine, but the new one is wider

SSE3+ & AVX{,2,-512} & co improve on SSE in pretty much the same way that x86-64 improves on x86 - the old thing still works just fine, but the new one is wider, adds new (very useful!) instructions, doesn't copy over others, and (at least partly) uses different encodings. And an important thing to remember is that there is and never as a single "x86" before x86-64; both Intel and AMD added new instructions as was seen useful in new generations. AVX & co just continue the pattern that's been going on for four decades.