As a photographer who routinely works with models, I have seen a lot of models lose out on potential gigs for the simple fact of what can be seen as "bad representation." Very rarely is the representation malicious, but simply a circumstance of the model and their representation are confused on what their roles are as it pertains to the model. Almost anyone involved in the entertainment industry will interact with one of the following or a combination of an Agent and/or a Manager. While many think that they are interchangeable, they are not, and they serve two totally different functions in a model's career. I will start simply with the Manager. The Manager's role in your career as a model is to simply MANAGE. They are there to make you better. If you need to learn posing, walking, speech, expressions and a list of other skills that are crucial to a model's development the main role of the manager is to arrange those critical events. A manager can also give you advice on how to handle your money, as well as what gigs to take or to pass on. A manager CAN get you jobs, but that isn't necessarily THEIR job, but that of the agent. What an agent should do though is promote you as much as possible. The Manager should be the one to organize your portfolio, comp cards, business cards, and other promotional material. A superior manager will have agents and potential clients seeking you out, as opposed to the other way around.
The agent's responsibility is to provide and arrange potential jobs for the model. Your agent is crucial as a liaison between you and an employer. Your agent's responsibility is to bring work to you. Simply put, if your agent doesn't find work for you to do, your agent doesn't get paid either. One thing to keep in mind, is that the agent/model relationship is a more of a two way street than with other support staff. In other words, an agent can not only be fired, but an agent can fire their client. One of the main reasons for being fired by an agent is simply refusing to work. If an agent provides you with several 'go sees' and castings, and you fail to show, an agent may drop you for conflict of interest reasons.
So what REALLY is the difference?
The simple truth is that ANYONE can be your manager. A photographer, another model, your mom, dad, boyfriend, girlfriend, spouse, or whoever can manage your career. There are no regulations that require any kind of training, accreditation or anything. The advantage of this is that ANYONE can be your manager. There are no hurdles to jump through to represent someone. And while managers, as well as agents, should only get paid when you get work, that's not always the case with managers. Some managers will ask for retainers for their services, and some will ask for about a 25% commission on your work. Once again an incentive to help you get work. One major drawback to managers comes from many don't have the experience to adequately represent you. They don't have the connections to schools, agents, courses, and other resources to be required. Also many managers may have a conflict of interest with your career if they are emotionally or intimately close with you. For this reason, I not only do I strongly advise against having a significant other as a manager, but I also strongly suggest that you should have a manager who manages other models. Their experience and desire to have a successful brand will almost always be to your advantage. Their desire to be successful will definitely be a push to you in the right direction.
An agent on the other hand, in most jurisdictions, MUST be licensed, and many have to be bonded and insured. Almost always, you will have a contract with an agent. An agent's job is to find work for you. A booking agent might even have a Power of Attorney, to be able to represent you on your behalf and to sign contracts in your name. An effective manager may have a POA as well, but be careful, there are no penalties for a "shady" manager, but there are tons of penalties for a fraudulent agent. An agent may require 10-15% of your earnings from gigs, as such; their desire is to keep you employed, as often and as long as possible.
Along with these two, you may have a business manager, a publicist, a brand manager/agent, or a whole slew of support staff, but the importance is to know the foundation and make sure it is a solid one. Hope this helps.