You can be:
Hospital employee-paid directly from the hospital, usually comes with benefits, malpractice, etc. Litlle/No involvement with billing/business aspects
University employee-in academic settings, similar to above but paid by the university/med school, obviously may include teaching, research responsibilities. Usually excellent benefits.
Independent contractor-often come without or with limited benfits, can work multiple places potentially for higher hourly rates. More complicated tax wise, must insure adequate malpractive. Can join a locums group that pimps you out and helps with licenses, job placements, etc.
Democratic group- You work with a group which bills for their own services, usually with a higher salary involved since there are less hands in the pot. The group must manage billing, insurance. All members have a say in the group. They will often hire temps to try them out at a lower salary with or without guarenteed partnership at a later date.
Contract management group- This is a company who gets a contract with a hospital to provide ED services. You then simply punch a clock for an hourly wage wth benefits provided by the group. A significant portion of your billed services are going to the management group as profit off of you. Must be careful as some these contracts have unfavorable terms like no tail coverage, or restrict your employement after leaving. Go to AAEM (not going to debate on here) about their concerns that this type of setting.
This is not all inclusive by any means but hope it helps.