My understanding, in a nutshell, is that an agent works for an agency and they get a breakdown of potential work in their specialty field (some agents work solely in commercials, some in voiceover and some in film/tv/theater, etc) every day. They take that list of auditions and match them up with corresponding actors they work with. They then set up auditions/appointments accordingly. These breakdowns will usually come from Casting Directors but can also come through producers and directors, too. The agent is the middle-man or connector between an actor and a Casting Director. They get paid by taking a commission (finders fee) of about 10%* of the actors pay-check. That is why on some job listings you will see the fee listed as $1000+10% so that the agent is accounted for in the final fee without eating into your gross pay.
A manager is a little more personal. They are technically supposed to be invested and focused on the career of the specific actor they are signed to. They are the middle-man/connector between an actor and BOTH agents/Casting Directors. A really good manager will have very strong relationships with top agencies and Casting Directors and will have their finger on the pulse as to the kind of material that is out there making sure to get you in the room with the right people. Managers generally get a 15%* commission. You will also owe the agent their 10% in addition.
I should warn actors starting out that there are a LOT of “managers” in New York. They can be unlicensed agents using the umbrella-term manager as a way to tap into the commission they can mooch off of an actor. They will demand a share of your earnings whether they help you get the booking or not. Do your research on both agents and managers when you find yourself faced with the option of working with one or both of them. You will NEVER, EVER have to pay an agent or a manager any other kind of fee up front or at any time. They work solely on the commission of jobs they find you.
* This is the industry standard but it is subject to the agency/managers agreement and can occasionally vary.
If you find a term that you don’t understand, please also check out the glossary. And, of course, feel free to ask me for anything I may have missed as the list is a work in process and I’m adding to it all the time.