it's basically the same but with 2-10 people (or more if you mod the game and extend this number).
usually when you play in multiplayer there are 2 options:
1) you go separately. meaning each does his stuff. then it's the same as single player but with more resources (for example you can find some copper and tin, while other players chopped some wood and got some meat\leather)
2)you go together: monsters become a bit more beefy (40%hp and 4%dmg per player iirc) but you have more people to deal damage. and you can do different things in combat: someone shoot from afar. someone tries to tank with shield. and someone is sitting afk nearby cuz he had a phone call.
2.1)as an exception there is another option: you may play mostly separately, but when someone dies(or you want to kill the next boss or build something) you gather together and do your stuff.

ps: multiplayer imho is best played with friends and\or voice. joining randoms may be harmful cuz they might happen to be griefers