That's not quite correct, v1 is regular spell haste, v2 is an older-era haste mostly found on Bard songs from the Velious era, and v3 is overhaste.
Ex, you're wearing a 43% haste item at level 60 you can have your haste buffed by:
v1: Example - ENC Wondrous Rapidity - 70%
v2: Example - BRD Composition of Ervaj - 10%
That would give you 223% haste (you start at 100%), which would be effectively 200% because it's capped at that. In this example a BRD running Composition of Ervaj is thus wasting a song slot since you're haste capped without it.
But then you could also use:
v3: Example - BRD Warsong of the Vah Shir (25% v3 Haste)
That v3 song is Luclin era though, but in the above scenario would take you to real effective haste of 225% if you had that running w/43% worn + ENC v1.
Due to how high most v1 Haste is (ENC WR is 70%, ENC epic is 66%, Bard epic proc v1 is like 66%), and most raiders have worn haste in the 40%+ range pretty easily you basically never need v2. The real use case for v2, sort of, was back in-era Velious when it was released getting those good haste items actually was a lot harder due to just vastly decreased gear availability. It wouldn't have been at all uncommon for even a raider in Velious to only have say, 21% worn haste from something like FBSS, or maybe a little more from something like a Sibilisian Berserker Cloak, Runebranded Girdle or etc. Even Cloak of Flames were rare/very expensive back in these times and a lot of people never did Plane of Sky. In that scenario the v2 stuff could help push you up to the 200% cap (before over haste), but even then it was usually such a marginal benefit that it wasn't super useful for Bards to really be using it much if ever.
Edit to add, so basically the formula posted by Foaming is 100% correct:
You get the highest of worn + V1(the super vast majority of spells/songs) + V2(upto 200% cap). How you achieve this is upto you. Then you can also get V3 (so called overhaste).
