Difference between a hydrated salt and an anhydrous salt?

A hydrated salt is made with the water molecule (H2O).
Anhydrous means no water.

A hydrated salt is a solid substance with water molecules contained in it. (Often the formula will be something like this: BaCl x 2H2O.) Hydrates have a general formula of salt + [x moles]water.

Anhydrous salt is basically a salt without water molecules.

When doing experiments, when you heat up hydrates, a certain amount of water will be released leaving the salt, also known as the anhydrous residue.

The difference is water.  A hydrated salt is one that has one or more (usually more) water molecules per salt "molecule" that are actually part of the crystalline structure of the salt.  Often when the hydrated salt is heated, and the water removed, (dehydrated) the crystal disintegrates to a powder of the anhydrous (literally, "without water") salt.

That occurs when copper (II) sulfate pentahydrate is dehydrated by heating it.  It goes from a pretty, dark blue crystal to a light blue to white powder.

CuSO4*5H2O  CuSO4 + 5H2O

Hydrated salt is a crystal salt molecule that contains water within it so in a chemical equation you would see Na Cl .10 H,2,0
While an anhydrous salt does not contain the water within it.

Differences is water vs no water