The main difference between Galettes and Crêpes is that Galettes are usually made with buckwheat and Crêapes with wheat. Galettes are a regional dish from the Brittany region of France but became popular all over France.
Especially for the versions typically filled with ham, cheese, and eggs.
I also recommend trying Crêpes in all variations (sweet, savory) and other regional dishes if you get the chance. Such as raclette and cheese fondue (Savoie), Bouillabaisse(Provence) Salade niçoise (Nice).