All space shuttles are spacecrafts, but not all spacecrafts are space shuttles.
A spacecraft is a vehicle designed to fly in outer space. Spacecrafts are used for a variety of purposes, including communications, earth observation, meteorology, navigation, space colonization, planetary exploration, and transportation of humans and cargo. A spacecraft is what landed America on the moon.
A space shuttle is something similar to a bus, in that it carries a crew and cargo, then returns after the mission is completed. In its spaceplane design, and series of ships were Enterprise (test model), Columbia, Challenger, Discovery, Endeavour and Atlantis. The Space Shuttle was only designed for low Earth orbit. It could not go into high Earth orbit nor escape Earth orbit to fly in deep space. It lands like a plane and would not be able to land on the moon.
There is a great size difference between shuttles and other spacecraft such as the Apollo Mission rockets.