하다 is infinitive verb 해 is 하다's order(command) verb

They're the same in meaning. The first one (하다) is just the dictionary form. This is what you would find in the dictionary. The second one (해) is a conjugated form of 하다. Explaining when to use them would require context. 하다 though would rarely be used by you though because it's the dictionary form. There is a conjugated form called plain form though that is very similar. You still won't really be using it. Not any time soon at least. You will mostly be using the conjugated form^^