I´ve tried to draw the difference between MVP and a Prototype on this picture. Simply put if you have a proof that your product is working you have a prototype. But you need to proof more than that to have a MVP.
You need to answer some additional questions like:
1. Who needs what you want to build and why they need that?
2. Are they willing to pay for it and how much?
3. Do I know where to search for those people and how much will they cost me?
Many startups go into the trap of working on proving that something is technically feasible (proof of concept) and developing the concept further (prototype) forgetting or postponing the work around checking for desirability and viability of their products.
In todays world I think most of the things can get done from a technology point of view (I am not talking about cancer treatment or other research heavy fields of study) so starting with POC or Prototype feels like starting in the wrong end to me.
Start with trying to sell your product (yes, without having it). Start working on your sales channels, and inside those testing different sales funnels, try to figure out the perfect combination of segment -> message -> channel.
The questions 1,2,3 above are much more critical to launching a successful product than the question of can we build the thing. The last part is usually the easiest one to answer.