Struts are a structural part of the suspension system on a vehicle, and shock absorbers are not. While both reduce spring movement, struts are also pivot points for the steering system and affect alignment angles. Vehicles have either struts or shock absorbers.
A shock absorber has internal valves with oil flowing through them. This oil flow slows down the movement of the vehicle's suspension. As shock absorbers age, the oil leaks out and they become less effective at absorbing suspension energy. This causes a rougher, more unstable ride.
A strut's internal design is similar to a shock absorber's, but since it's part of the suspension system, it has a different exterior construction. Like shock absorbers, struts leak oil as they age, which leads to the same issues. A strut typically has a coil spring around it. The mount on this spring can rot away, in which case the spring stabs the tire.
Shock absorbers and struts tend to deteriorate considerably after 50,000 miles, at which point the owner should replace them. Struts are typically more expensive to replace, and an alignment is necessary when replacing struts. However, certain struts have a replaceable cartridge section inside the body of the strut. This allows the owner to replace the portion of the strut that handles shock absorption without removing the struts or performing an alignment.