Strut has the spring as an integral part of it the shocks are just the dampening mechanisms. Usually in a shock you have leaf or torsion bars in a truck or traction bars like the fiat 500. Cars like ours have a coil spring that go around the shock, and the shock has a mount to support the spring making them struts. Hopefully this clears the confusion. You were actually quite close as at least you knew the two aren’t the same.