In general, a strut is a functioning member of the support of the vehicle. A structural device holding the vehicle relative to the tire.
A shock absorber is a dampener to spring movement/oscillation.
In some cars a shock absorber is built into a structural member and that is refered to a a strut. A strut doesn't have to have a shock in it; such as a longitudinal strut.
More simply put, a car wil roll down the road without a shock but will fold up without a strut.
Bosch Master, ASE Master, L1
33 years MB technician