What service program is required for a generator? None, specifically. What service program is required for an alternator? None, specifically. Refer to the particular item for AD's or manufacturer maintenance publications...but if it's being operated Part 91, it's an on-condition item regardless of weather it's a generator or alternator.
From your perspective, you wouldn't know the difference in the cockpit. An alternator puts out stable voltages at lower RPM's, whereas a generator output increases with RPM and may be unstable or unreliable at lower end minimum values. Alternators are generally lighter, but usually not designed for the large capacities that generators can handle, for various reasons. Today, most light airplanes use alternators (not all), and most large aircraft with high electrical demands use generators. (Also, in many cases for weight issues, as the generator first functions as the starter during engine start, and is called a starter-generator).
Often in aircraft literature, the electrical generating device is referred to as a generator (correctly so), regardless of weather it's a "generator" or an "alternator." This may be confusing you. It's generating DC current output,and that's all you need to care about. The alternator generates alternating current which is filtered through a rectifier (usually internal diodes) to allow only a DC output...but the result is the same to you, the user. You get DC power to run your electrical system.
Pilot handbooks do sometimes confuse the terms, and correctly refer to the electrical generating device as a generator, even if it's an alternator. If you want specifics on the device, go look on the airplane to see what you've got, and review the aircraft maintenance publications. Some light airplanes are type certificated with a generator, but outfitted via STC at a later date with an alternator (Cessna 140, for example). This mostly applies to older aircraft.
For a quick check, visit your airplane on the line and look. If it's got a clunky black solid looking tube with a few small square holes at the back, it's probably a generator. If it looks like a little silver bird cage with lots of long holes and wires and spinning things inside, you're probably looking at an automotive type alternator.