Difference between recursive and system with memory
you can have memory of past outputs.  thems would be $y[n-1], y[n-2]...$  and you can have memory of past inputs which would be $x[n-1], x[n-2]...$  and you know your current input $x[n]$.

if the output you're trying to compute, $y[n]$ will depend on any of the past outputs, it is recursive.  if not, it is not recursive.

if the output, $y[n]$, depends on any past outputs or past inputs, then it is not a "memoryless" system.