In a nutshell, a full floating axle has independent and hub assemblies. This allows the hub to carry the full weight of the vehicle and the axle only transmits power. If you look at the ends of the axle, there are 8 bolts that hold the axle in the hub. This is the stronger of the two.
Semi float rear axles have the wheel hub on the end of the axle so they are one piece. C clips in the carrier hold the axles in place. While still pretty strong, the axle supports some of the vehicle weight, as well as transmits power.
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