The difference is already referred to on the Mage's Ballad (and other songs tied to the BRD dots) skill card.....
The 20% ones proc off Venomous and Wind bites, while the 40% ones are proc off Caustic and Storm bites, of which are level and sync dependent.
In a sense, the songs become the "Version 2" once your L64 Passive Trait "Bite Mastery" is active, which becomes so at L64 with a BRD job stone equipped.
At any time your level is synced below L64, then you no longer get the Passive Trait effect, which then reverts every other Skill or Trait that is tied either directly or in the case of Bard Songs indirectly to it to the "lower version" of which will then reflect on the skill card in question.