In the post originally termed: "What is the difference between a causal system and a memory system?", someone corrected the term "memory system" to "memoryful", as opposed to memoryless. And this was validated (while I was hesitating, way to long, to modify or reject the edit). I threfore suggested in comments that "memory system" or "non-memoryless system" were the only versions I have heard of.
But... what shall we do?