"He scheduled to move to Amsterdam" isn't actually correct. You could say "He is scheduled to move to Amsterdam."
A "schedule" almost always involves an element of time. A train schedule doesn't just tell us the train's destination, it tells us when it will get there. "The project was completed on schedule" means it was finished by the promised time.
A "plan" often means a detailed series of steps for accomplishing a goal, but there may not be any times stated at all, or the times may be approximate. For example, "we plan to fly into Logan Airport, take the Silver Line to South Station, and then take the train to Norfolk." ("How long will that take?" "I don't know, I haven't looked at the train schedule yet.")
"Schedule" can be a noun, or it can be a verb meaning "to make a schedule" or "to include something on a schedule."
"Plan" can be an noun, or it can be a verb meaning "to make a plan."