The best way to think about the Coast Guard is to divide it into three parts. One part is the cutter fleet. One part is aviation. One part is the sector community.
Cutter Fleet
These are the guys and gals on ships more than 65 feet in length. For officers the cutter fleet to you will be 87' - 420' cutters. Within the fleet there are little sub-communities, based on the hull colors. White hulls comprise the majority of the fleet. These are the cutters you see often enforcing fisheries laws, interdicting drugs and migrants and conducting search and rescue. The larger white hulls (210' and up) also have flight decks. Black hulls are typically Aids to Navigation (ATON) boats. They're buoy tenders. Yes, they can do other things, like search and rescue, enforce laws etc, but their focus is typically ATON. There are also a small number of 140' ice breaking tugs that also are black hulls. Red hulls are the last community and it's a small one. The red hull community are ice breakers. There's the 240' Mackinaw on the Great Lakes (which is more like a big buoy tender that can also break ice), the two 399' "Polar Rollers" Polar Sea and the Polar Star (but one is in dry dock... and being used for parts) and the 420' Healy. Healy and the Polar Rollers also have flight decks. These larger ice breakers are typically engaged in scientific operations.
Aviation
This is pretty straight forward, this is the community that flies. It can be broken down into two main sub-communities; helos (helicopters) and fixed-wing (planes). In the helo community you have the MH-60 Jayhawk, which is the Coast Guard's version of the Blackhawk, and you have the MH-65 Dolphin. Because of its size, the MH-60 is typically landbased (it's too big for the flight deck of most Coast Guard cutters), while the MH-65 can deploy with cutters, but also have home Air Stations. On the fixed wing side you have planes that typically support search and rescue operations, transport Coast Guardsmen and act as an "eye in the sky."
Sectors
This is the land-based portion of the Coast Guard. It can reasonably be divided into two sub-communities, prevention and response. Prevention is essentially inspections. They'll inspect cargo or commercial vessels, make sure they're up to standards. Response is your small boat stations and boarding teams. They'll go out and board vessels, provide port-side security etc. I think a Sector Commander (Captain of the Port) is one of the most powerful operational assignments in the Coast Guard, and maybe the military (note, I'm saying operational, obviously flag officers have more "power"). They can close down entire ports, on their own authority (it doesn't happen often). While that may not seem like a big deal, in some very large ports, such as NY, or Los Angeles Long Beach, etc. that has a HUGE impact on commerce.
So these are the operational communities. Outside of these communities are other communities. Your career will move from operational assignments to staff assignments (staff assignments are more like desk jobs). Eventually you can develop two career paths, your operational career path in one of the above communities, and a staff career path... in an area you've had some experience and expertise. Staff and operations tours can be related. You may be an officer on a cutter and then go to Coast Guard HQ in D.C. and work in the Cutter Forces office as a staff tour.
Hope that makes sense. Let me know if I've thoroughly confused you.