OK465 pretty much has it, certainly Cessnas and Pipers that are cleared for spinning are VERY prone to ending up in a spiral dive instead of a spin, recovery from a spin is unlikely to over stress the aircraft unless the pull out is delayed or MUCH too slow, spiral dive recovery is much more likely to cause over stress.
Proper spin training will teach you not only spin recovery, but how to recognise if it is spinning or spiralling - it can be surprisingly difficult to tell the difference just by how it looks outside.