Motion and Movement ?

Hi guys ! I'll make it brief.

I'd like to ask about the difference between the nouns Motion and Movement. I was doing an English exercise and I saw this "At a single ... of his hand, the room fell silent." And there are two choices : Motion and Movement.

My teacher told me the correct answer is "Motion", because in this case, "motion" is considered "gesture", whilst "Movement" is simply "a change in position". Also, the Oxford Advanced Learner Dictionary has the same sentence as an example for the word "motion".

I have looked up many dictionaries from Oxford Advanced Learner Dictionary, Oxford Dictionary of English,... and even Google. But the answers in each site are different, some say "the only difference is their popularity", some say "motion is a more scientific term". Some say "movement is mainly used when you talk about the body or body parts".

The thing is, I think we can use "Movement" too. So, am I right or am I wrong ? Please help ! Thanks !