suspend: a very temporary thing

We've temporarily suspended the production while we figure out what's causing this problem.

stop: a little bit more serious; it could be for a longer time.

We've stopped production on this new car, because it's caused some accidents.

shut down: feels pretty permanent;

We've shut down this factory because of repeated health violations.

But they are kind of interchangeable, we can use them a bit more flexibly. They're a little bit connected, they overlap with each other.