In most instances they mean the same thing, but not always. I can say that an area is restricted, it means you can't go in that area. However, I would not say the area is restrained. People are restrained (by rule or by barriers) from going in, but you can't use that word about the area itself. Also, if a policeman puts handcuffs on a person, that person is said to have restraints. Technically, you could say that the person is restricted, but you would never hear that - the closest would be to say that the person's movements are restricted.

They come from the same root word in Latin, but to me "restrict" may allow some movement within limitations (though not always), whereas "restrain" acts directly on the person or thing being limited or prevented.