An agent is someone legally qualified, contracted by you, to seek out work for you and act as a “middleman” between you and your prospective employer. They usually take around 10-15% from your contracted fee for the service. Agent fees in California are limited by law to no more than 10%.
A manager has no legal rights to make deals for you. They also have no cap on what they can charge. Managers are mainly for career guidance, financial planning, legal advice (to a degree) etc. The manager-client relationship is usually much closer than an agent-client relationship as agents will often have thousands of clients under their wing. Managers usually only have a couple. Most managers will deduct 15-20% for their services, although there is no legal limit set for their fee. They may add extra charges for such things as legal services used to “execute a deal”, time involved in servicing the client’s needs etc.
You can get lists of reputable agents and managers from the various trade guilds in the relevant industry discipline.