how is a memory-resident part of an operating system different from a non-resident part of an operating system

Answer 1

Operating Systems are big, and you don't want to keep the whole thing in memory, or it would not work on computers with small memories.

However, certain parts of the operating system are used so often that you don't want to page them out of memory, because the performance would suck. So those chunks of code you put in memory-resident sections, and they are never removed.

A perfect example is the code that handles paging. If it gets paged out, it will never be executed to get paged back in. So it better be memory resident.