The CPU has registers, but doesn't the RAM have registers too?
In a sense, you are correct. The registers in a CPU are the fastest, most expensive type of memory and very similar (possibly even identical but more likely optimized a bit differently) to tightly coupled memory, cache, and on-chip static RAM.

In a very high-level sense, registers are not placed in  big blocks on the silicon die like other on-chip static memory (I think, someone correct me if I am wrong). They are placed wherever they are needed by the peripherals and logic they are associated with.

Not dynamic RAM though.