These all refer to the type of transistor used
Bipolar- amplifies current, rather than voltage. Generally sound "fast" and detailed, but also tends to give the cold, analytic sound people associate with solid state... not very good for input stages, when used properly can be great as an output stage...
JFET and Mosfets are a different type of transitor (field effect transitor), which amplify voltage, so designs using them are similar to tube circuits. Jfets (junction-fet) use traditional silicon, while mosfets use a metal oxide semiconductor... Mosfets are known for their warm, smooth sound, but can also be noisy and lack clarity ("vieled")... Jfets have a sound inbetween mosfets and bipolars, and are commonly used on the inputs of amplifier circuits...
All of these just describe the type of transistor used, and have nothing do to with the design of the amplifer. Designs frequently use more than one type (maybe even tubes) for the best sound. Also, the topology of the amp has a huge effect on the overall sound, so it's possible to get a warm/smooth bipolar amp or a fast and analytic mosfet amp