Well, they are both the effect of external magnetic field on currents flowing in a conductor. And they are both consequences of maxwells equations. So they are both coming from the same basic physics and I am not sure you can make a sharp distinction between them. That said, there are a number of differences in scenarios that are usually considered:
* In the proximity effect, the "external" magnetic field is thought of coming from a nearby wire, often part of the same circuit. In the hall effect, it is usually applied externally
* In the proximity effect the important factor is the distribution of current in the offended wire. With the hall effect we are normally concerned about the transverse emf / voltage measured across the conductor. Of course, that EMF is what pushed the current distribution around.
* An important characteristic of the hall effect is that the charge carriers are always pushed in the same direction regardless of sign. This means that the sign of the emf depends on the sign of the charge carrier: this is important in semiconductors where p-type semiconductors are dominated by positive charge carriers. We don't normally care about this distinction when talking about the proximity effect.
* The hall effect is also commonly talked about in quasi 2D systems where you can get fun effects like the quantum hall effect, the Aharanov-Bohm effect, and so on. These can't be simply related to the concepts normally considered "proximity effect"
So basically they are two different ways of thinking about the same underlying physics.