Praise be to Allah.
The difference between pillars (essential parts) and obligatory parts of prayer is that the pillar or essential part (rukn) cannot be omitted deliberately, by mistake or out of ignorance, rather it must be done.
The obligatory part (waajib) may be omitted due to ignorance or forgetfulness, and it may be compensated for by doing the prostration of forgetfulness (sujood al-sahw).
There are fourteen pillars or essential parts of the prayer, and eight obligatory parts.
They have been explained in the answer to question no. 65847.