Isn't it true that if an algorithm can be tail-call optimized, it can be rewritten to not use recursion at all? (And conversely, if something can't be rewritten

Isn't it true that if an algorithm can be tail-call optimized, it can be rewritten to not use recursion at all? (And conversely, if something can't be rewritten without recursion, it can't be tail-call optimized?)