All pages in the end are considered for being swapped out. In Linux it starts by swapping out freeing cache pages followed by clean non-recently used pages (which just requires unmapping rather than a write to the swap device). After this it will try to flush dirty file backed pages in memory to their respective backing device before finally reaching the point where it must starts swapping anonymously backed process pages (includes stack, data that can be edited, heap, etc....). Any non-kernel page is always a candidate for being swapped out it just depends on the memory pressure on the system.
Pages that already have a backing store are simply unmapped or if they are dirty are flushed to their backing store. They are not written to swap for obvious reasons.