Adapter: Just lets your plugs - the physical shapes - work with their sockets. Does not do anything to the electricity. Small, cheap, available everywhere, just little bits of plastic and metal and a tiny bit of wiring. You will want to bring one.
Converter: "Converts" THEIR (more powerful) electricity down to use our devices (without making them go "poof" with a spark and a small puff of smoke, potentially starting a fire and other Very Bad Things). Heavy, bulky, somewhat expensive, but heavy heavy heavy and usually completely unnecessary for almost all consumer electronics. It would be hard for me (and most people, I think) to justify lugging a converter around the world.
Most popular small consumer electronics (or their chargers) work fine on European electricity and usually just require an adapter for the plug. The exception to this are 1) anything very old, and 2) anything that "makes heat" - like a toaster or...hair dryers. For a phone or camera charger, you probably only need an adapter plug. If you want to microwave your lunch or bake anything (including your hair), then it gets more complicated.
I don't have enough hair to have any relevant experience with hair dryers, but I've heard that so-called "dual voltage" blow dryers may not be quite as dual-voltage as one would hope. Best to ask others about that. Be careful about plugging in anything that makes heat. Charging your phone? Knock yourself out and party on.