Multi-purpose bars are great for general training, Crossfit, etc... They generally have a thinner shaft diameter and dual knurl rings, which makes it possible to perform a variety of lifts. They spin using bushings, bearings, or a combination of both depending on your preferences. For example, someone who mainly uses the bar for olympic weightlifting may prefer a 28mm shaft with bearings. Someone who mainly uses the bar for powerlifting may prefer a 28.5mm shaft with bushings.
Power Bars are made specifically to perform powerlifting movements, including the squat, bench, and deadlift. They may also be used for other movements like the overhead press. These bars typically have a 29mm shaft, which creates a very rigid bar, but some offer a 28.5mm shaft. They also include a more aggressive knurling, single powerlifting knurl rings, and they use bushings to spin.
Olympic Weightlifting Bars are made specifically to perform Oly movements like the snatch, clean & jerk, etc... They generally include a 28mm shaft diameter, which generates more whip (flex). They include single weightlifting knurl rings and they use bearings, bushings, or a combination of both to spin.