Separating different parts of a program into different processes seems (to me) to make a more elegant program than just threading everything. In what scenario would it make sense to make things run on a thread vs. separating the program into different processes? When should I use a thread?
Anything on how (or if) they act differently with single-core and multi-core would also be helpful.
You'd prefer multiple threads over multiple processes for two reasons:
Example:
Applications with GUIs typically use one thread for the GUI and others for background computation. The spellchecker in MS Office, for example, is a separate thread from the one running the Office user interface. In such applications, using multiple processes instead would result in slower performance and code that's tough to write and maintain.
You sure don't sound like a newbie. It's an excellent observation that processes are, in many ways, more elegant. Threads are basically an optimization to avoid too many transitions or too much communication between memory spaces.
Superficially using threads may also seem like it makes your program easier to read and write, because you can share variables and memory between the threads freely. In practice, doing that requires very careful attention to avoid race conditions or deadlocks.
There are operating-system kernels (most notably L4) that try very hard to improve the efficiency of inter-process communication. For such systems one could probably make a convincing argument that threads are pointless.