QFI / CRI are both qualified instructors, but differ in who they can instruct. A CRI is a qualified instructor, but with a more specific role/scope.
As there is no such thing as a QFI outside of the military it is a bit of a moot point!!
We have
FI
CRI
TRI
IRI
SFI
But no QFI. All of the instructors listed above are QUALIFIED Flying Instructors of one flavour or another.......
Sorry XX - I could not resist the foray into pedantry, your post is quite correct.