What is the differance between a car carrier and broker?

Carriers

For starters, you can perform a search engine query under "car carriers." Select the ones you may be most familiar with. These are some of the larger companies, which also may have some sort of association, typically via sponsorship with a large online or nationwide auction house, or maybe active with your specific car club.
Virtually all auto transport companies offer a "free quote." This is a very quick and painless exercise in determining the cost of shipping your vehicle and can be done online. You risk very little and shouldn't be worried about providing your email address to them. This is necessary for the carrier in order to respond. Generally, quotes are delivered within 24 hours, 48 max. The actual process simply involves listing the zip codes: where the vehicle is currently and where it will end up. You include your name, if you want, but at least an email address and the dates when you want the vehicle transported. A proper, professional response quickly appears and you've got your first rate. Then do it again with several other shippers to compare fees.

Brokers

The first thing you have to take into consideration is that there are transportation companies and then there are brokers. Nothing wrong with either one, except that a broker typically is just that—he doesn't own his truck (or trucks), but negotiates with other companies that may need to fill a rig bound for a certain destination. The trucker is looking to fill that hole, so there is some "wiggle room" in his fee. You don't know that, but the broker does, and this is where he makes additional money. You can recognize a broker if he typically asks for a deposit up front (most of the time this is non-refundable), with the balance to be paid upon delivery of the vehicle. The advance is what the broker keeps; the balance is what the driver/shipper makes.
If you're evaluating all sources based upon price, you have to factor in several other key points:

Options

Ship open or enclosed? That depends on how valuable your vehicle is. Enclosed units protect your vehicle from all road hazards and weather throughout transport. That is a good thing. Your vehicle arrives, hopefully, without a knick or scratch, not to mention the noticeable lack of bugs on the grille or windshield. This is generally the most expensive option in auto transport.
The next level of shipping is an open multi-car unit that transports vehicles on upper and lower racks. This method of hauling is commonly used by automobile manufacturers to move vehicles from factories to dealers, but individual owners can utilize them if they are shipping unrestored collector vehicles or their everyday (leased, perhaps—) cars. This is obviously a less expensive transport option.
There are still more economical ways to go. In most instances, you will specify that your vehicle go "door-to-door." The transporter comes to the home or office of the person or company/auction house from whom you purchased the vehicle—assuming you have coordinated this in advance with said party—and will collect the vehicle. Then it will deliver your darling right to your home, garage or storage facility. This service is worked into the overall fee.