What is the difference between a 'page' of memory and a 'frame' of memory?
Short version: "page" means "virtual page" (i.e. a chunk of virtual address space) and "page frame" means "physical page" (i.e. a chunk of physical memory).

That's it, pretty much. It's important to keep the two concepts distinct because at any given time, a page may not be backed by a page frame (it could be a zero-fill page which hasn't been accessed, or paged out to secondary memory), and a page frame may back multiple pages (sometimes in different address spaces, e.g. shared memory or memory-mapped files).