The fundamental difference between an FI and a CRI in EASAland is that a CRI can only teach someone who already has a licence (a ME class rating is a good example of stuff that can be done by a CRI).
He cannot take Joe Public off the street and train him/her for a licence.
An FI, when suitably experienced and appropriately qualified, can do everything that a CRI can, but it doesn't work the other way around.
HTH
DD