V1 was the initial version of Plutus, introduced in the Alonzo hard fork.
V2 was introduced in the Vasil hard fork.
The main changes in V2 of Plutus were to the interface to scripts. The ScriptContext was extended to include the following information:
V3 was introduced in the Conway hard fork.
The main changes in V3 of Plutus introduce:
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The Cardano ledger tags scripts with a language that determines what the ledger will do with the script.
In most cases this language will be very similar to the ones that came before, we refer to these as 'Plutus language versions'. However, from the ledger’s perspective they are entirely unrelated and there is generally no requirement that they be similar or compatible in any way.