To elaborate on Andrea's explanation with my own biases:
A stationary bike resembles a beach cruiser (bike). You sit upright and lumber along with a slow cadence (rpm). The saddles are huge! It can be a good workout but it tends to be quad heavy. The computerized bikes (like a Lifecycle) are just stationary bikes with some fun programs that are nice & distracting.
The other end of the spectrum is putting a real bike on rollers (hats off to you) or a "trainer". A trainer is just a stand for a regular bike so you still use whatever gears, pedals, etc the regular bike has. Trainers vary in noise & stability. They're usually easy to fold-up (the trainer, not the bike) & they're much cheaper than a spin type bike.
A spinning type bike (Spinning is still trademarked) has the stability of a stationary bike so that you can stand & otherwise have an intense training session. The "gears" are actually a very heavy front wheel with variable tension. You use a knob to change the tension which can also serve as a brake of sorts. They are still pretty loud and they are heavy. It's not a piece of equipment you'll want to move very far. The bikes geometry mimics an outdoor bike so they're a great training tool for outdoor cyclists and anyone else that wants a great lower body & cardio workout.
Debra