There are a number of broad elements that distinguish all types of stationary cycle, and there is considerable overlap between these elements with the different models available. Most broadly, these are (1) fixed and free hub, (2) contact, air, and/or magnetic resistance, and (3) chain or belt drive. No element is inherently superior or inferior, but they do present different riding and performance characteristics. The distinction between them is largely a matter of need and personal preference.
Perhaps the most glaring component is the hub. ‘Spin’-style cycles have a fixed hub linked to a flywheel, usually by a regular bicycle chain. These cycles essentially simulate a track bicycle or ‘fixie’, forcing the rider to pedal or ‘spin’ continually—hence the name. The mass of the flywheel, typically in the order of 11 to 16 kilograms, presents the greatest difference to riding characteristics. A lighter flywheel is more responsive, but it is also affected more by the resistance—contact (e.g. felt brake pad) or magnetic. The mass of the flywheel should ideally be matched to the mass of the rider, since its purpose is to simulate the his/her inertia.
Free-hubbed cycles, such as wind trainers or magnetically-resisted commercial models, more closely approximate road cycling insofar as the rider can stop pedalling at any time and just ‘coast’. The flywheel on these models is typically light, which results in their having very little inertial resistance. Virtually all of the resistance is provided by the wind vanes or magnets—and that resistance is a function of, amongst other things, the angular velocity of the flywheel. Consequently, these cycles feel comparatively ‘light’ and responsive, with the resistance increasing gradually as a function of effort.
This highlights one important distinction between the performance characteristics of the resistance mechanisms. The resistance of contact brakes is greatest at zero angular velocity (i.e. when the flywheel is stationary), then decreases once the flywheel is moving. By contrast, the resistance of wind and magnetic brakes is proportional to velocity: the more quickly we cycle, the greater the resistance. Neither of these mechanisms simulates riding conditions entirely accurately, however, since pedalling resistance in the real world is not a function of cadence but of other factors such as relative wind velocity, wheel speed, and surface gradient. Thus, they can only approximate real-world cycling.
Contact-resisted ‘spin’ cycles feel most natural at high (80+ RPM) cadences. However, they tend to feel unnatural during low-speed, high-torque training, since the brake pad tends to ‘bite’ excessively, giving a feeling of push-brake, push-brake with each stroke. Magnetically-resisted ‘spin’ bicycles largely circumnavigate this limitation by providing angular-velocity-dependent resistance. Both simulate track conditions with a fixed hub and heavy flywheel to approximate rider-bicycle inertia. Magnetic- and air-resisted free-hubbed cycles more closely approximate road-riding conditions, but cannot simulate the inertial forces associated with starting from a standstill or from large accelerations. The better choice will depend on the style of riding that you favour.
Belt drives are considerably smoother and quieter than chain drives, but they may feel unnatural for more ‘serious’ cyclists. Both contact and magnetic resistance is associated with significant noise—the former issuing a whirring sound and the latter a fizz—with magnetic resistance generally the quieter. Wind resistance is far noisier, emitting a constant high-pitched hiss. Belt-driven magnetically-resisted machines, like the high-end commercial models found in gymnasiums, are the quietest overall. However, a well-lubricated and maintained chain-driven unit can also be relatively quiet, and may have the perceived advantage of more closely simulating a real bicycle.
Finally, non-commercial magnetically-resisted cycles can theoretically develop adequate resistance for any level of rider, and there are non-commercial models that offer excellent variability of resistance. However, most models have been designed with a lower-performance rider in mind, and even those which can offer the resistance may not necessarily handle the heat generated by long bouts at that resistance. (A rather excellent non-commercial Cateye cycle that I used some years ago began to smoke after about 25 minutes of pedalling at a very high resistance.) I strongly recommend shopping around and trying the various models before making a purchase.
As an addendum, it should be noted that ‘spin’ cycles tend to represent better value for money at the lower end. Good examples are of stiff, heavy construction and have components that are compatible with standard bicycle parts. Thus, they can accept clipless pedals, a new saddle, or the handlebar of our preference. Low-end free-hub cycles are typically of lighter, more flimsy construction—and even many high-end ones do not offer component compatibility. For serious use, a low-end ‘spin’ cycle is invariably preferable to a low-end free-hub cycle.
I hope that is helpful.