Is it allowed to connect 14 awg ground wire to 12 awg ground
Assuming US here.  

As long as there are both 12 gauge and 14 gauge grounds going back to the (same) electrical panel, that will be fine.  The reason for this, is that if something shorts out, it will take the "path of least resistance" to ground.  If there is at LEAST a 12 gauge and a 14 gauge path to ground, the 20 A and 15 A circuit will each have "big enough" paths to ground. (actually, now the path to ground is even bigger, assuming that the two circuits don't short at the same time).