How do these branches of Buddhism differ?How does Therevado, Mahayana, and the Vajrayan Buddhism differ?
Therevado, Mahayana, and the Vajrayan are not Buddhism, but different societies who assume to represent (agents) and study Buddhism from their school of thought. It is important to note that few in these societies have access to the core of Buddhism. Rest are just not-too-smart marketing force.
In There+vada or Hinayana (meaning little vehicle), student strictly should learn from adult monk (teacher) = memorize with no argument. Therefore, less scope for research & less distortions for Dhamma. Monk interpretations of Dhamma is so poor & hypocrisy + contradictions exist.
Maha+yana meaning big vehicle has done many research & somewhat distorted Buddhism as a result of the bulk (uncontrolled fictional interpretations cause to reverse Buddhism).
Interestingly, Vatican has a backdoor to Tibet underground, especially to articulate world wars (wars between worlds)!
The core of Buddhism remain as to the opposite of nyaaya (recursion), where detach from the system game to avoid loss.
Use these societies as tools to study Buddhism, but do not be blinded to surrender to them. They are master spell binders!