Right, though the LD? and ST? instructions were kind of exceptions. You could only do arithmetic and stack and bitwise ops (and, or, eor, shift, rotate) with A, never X nor Y. Increment and decrement were X/Y only. You couldn't even add two registers together without stashing one in memory.
You had LDA and LDX and LDY as separate instructions while the Z80 assembler had a single LD instruction with different operands. It's the same thing really.