A fixed bridge is fixed to the body of the guitar.
A floating bridge floats over the body. Basically it's held in place by the string tension above and spring tension underneath. If you've seen a Fender Stratocaster/Ibanez RG guitar, they all have a floating bridge.
A vibrato/tremolo arm/whammy bar is connected to the floating bridge to allow you do change the pitch by either pushing the bridge down (reducing string tension) or raising the bridge (increasing string tension). Doing this in rapid alternation is called whammying.
Floyd Rose is a type of floating bridge.
Non locking tremolos are the floating bridges that don't let you lock the strings, so frequent use of the tremolo can affect the tuning. Locking tremolos let you lock the strings in place so that you don't lose your tuning.
You can google the terms, the internet isn't always full of lies.
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