What is the difference between an IRCOp and an Admin?

An Admin actually runs a server. He/she almost always either owns the hardware the servers runs on, or has physical access to it. The Admin has all final decisions about server-related matters, like who is an IRCOp, what they are allowed to do, whether bots are allowed, etc. The Admin is probably an IRCOp, but it is not required for him/her to be.