Geometric dual is abstract dual for plane graphs. G has abstract dual iff G is planar. So abstract dual can be geometric dual or some other bijection.
But I guessed if G is planar and connected maybe abstract dual is always geometric dual. This might be true or false, but I have another question that if there is a condition that makes this proposition true. (eg. connectedness, 2-connectedness, etc...) Can you explain if there is?
“Whitney showed that the geometric dual graph and combinatorial dual graph are equivalent (Harary 1994, p. 115).” - Wolfram Alpha