Digimon Masters/Mechanics

Burst Mode
Burst Mode is an, evolution you need an item (that you have to buy with Silk or Premium Silk) to unlock that evolution. For example the burst mode of Beelzemon (wich is not really a burst mode: it's a side form) is Beelzemon Blast Mode wich he needs a "Toy Gun" for.

Facts
Most of the "Burst Modes" in DMO are not real BM's mostly they're just side forms or just an Evolution where you need to buy an item for.

Drive Mode
A Drive mode is just the same as a Burst mode only when you unlock a Drive Evolution with an item you can ride it. For example Beelzemon needs his "Behemoth" to unlock his Drive Mode or Gallantmon and his "Grani". Some Digimon are rideable without a special item instead of that special item you need a Rider Wing wich you can buy at some NPC's or ModeSelector wich you can buy with Silk or Premium Silk.