A constraint is a boundary within which you must conduct your project. You might have to use certain staff, or you might have a limited amount of time, or you may have to use a certain technology, or you might have to be located within 5 miles of a site. Those are all constraints.
A dependency is a specific thing that must be done (or started) before another thing can be started (or done). It's a sequencing thing. You must select a project manager before a project management plan can be created. You must design a boat before you can build it. You must have a customer before you can make a sale. You must have a ticket before you can see a movie. Those are all dependencies.
You could view a dependency as a constraint, but doing so probably blurs both.