Absolute potential vs potential difference - what's the difference between the two?

Only differences in potential are physically meaningful.  The absolute potential is not measurable.

Think of it in terms of gravitational potential energy.  Only differences in height provide the information we need to calculate, say, how fast a roller coaster goes at the bottom of a hill.  We don't need to measure how far away the roller coaster is from inifinite distance, or how far it is from the center of the earth (though we could *define* an absolute scale of gravitational potential in either of these ways, or by the more common convention of setting 0 to be at ground level)  These different possibilities for the absolute potential provide a method for calculating it.  But in any physical problem, the choice of the 'absolute' potential doesn't matter, because only differences in potential will result in things that are measurable.

There really isn't much of a difference.  Potentials of any kind are always relative to some base level.  When that base level is zero, we can call it absolute potential.  When that base level is other than zero, we can call it relative potential.  But both types represent an interval value, not a point value.  Which leads me to assert there really isn't much of a difference.

By the way, there is nothing theoretical about this.  This is just definitional, which is why I say we can call it "blank" potential, but we don't have to.  What we have to do, though, is be consistent once we do define the potential.  That is, once the base line is set, keep it there until the problem is done.

The other answer is correct.  We typically designate a given base line as the zero base line.  It isn't something that just naturally occurs.  But, again, once that zero base is designated, it needs to stay there for consistency until the problem solving is done.