As I understand it, when processes are swapped-out of main memory and then back in, they can occupy different regions of physical memory. Is this ability shared by all three of segmentation, paging, and partitioning memory management systems? If not, what are the differences and why?
You are mixing a lot of of different concepts. Segmentation is an obsolete system for managing memory. In ye olde days when a large system had 1–2 MB of memory and 16-bit addressing, a process could only access a fraction of the system memory (64Kb). Segment registers were used to access larger address ranges (at different times). Segmentation could be used to support multiple processes or it could be used to increase the available memory in a single process. While the process was limited to 64KB at any one time, playing with segment registers would allow a process to have more than 64KB of memory (total) available to it. This was a common practice on PDP-11s.
Partitioning and segmenting are essentially the same and are equally obsolete. I described the PDP as using segments. Others describe it as using partitions. There are multiple versions of partitions.
Intel kept (and keeps in 32-bit mode) segmentation alive long after it should have died out in its processors.
Swapping is an obsolete system for implementing multi-processing. The entire process gets moved to disk. In the days of 64KB processes this did not have the overhead that moving a 32-bit address space to disk would have.
Modern systems use paging for memory management. In virtual memory systems, individual pages are moved to secondary storage; not entire processes (although it is possible for an entire process to be paged out of memory).