Yes, there are specific healthcare recruiters for each region of the country for each branch; the branch website usually has drop down menus that guide healthcare professionals to the right recruiter. I'm not sure whether you can really join with an associates degree or not. That seems to fluctuate based on need for nurses and I know the Air Force never allows it. Typically if you can, you are required to get a BSN before you can promote to a certain rank...usually O-3 or so.
The difference between branches for those who are military nurses is small. You still have the one weekend a month and 2 weeks per year requirement. You're job is largely nursing focused. The finer job details and mission will vary by branch. With the reserves/guard, you interview with each unit; this is similar to a civilian job. Each unit typically has a certain function, and those functions differ by branch. For example, the Air Force reserve and guard units generally focus on aeromedical evacuation and patient movement by air throughout the world: flight nursing, staging, etc. You really have to ask the unit what they do.