A mitre join is when the edge of the stone bench top is cut at a 45 degree angle. Another strip also cut at 45 degrees is glued to this edge to form a 90 degree angle. Mitre joints look more seamless, they are more labour intensive and therefore more expensive.
The butt edge is where the vertical side of the bench sits under the horizontal stone slab. Though cheaper, this is often preferred for its simplicity.