My understanding is that a bonded job usually means that the company fronted up money to sponsor the worker/employee for higher studies or specialised training.

I was bonded to MOH after my overseas training programme ended for 3 years, and if I broke the bond, not only would I lose my bonuses etc, I had to pay back the amount that MOH spent on me.

A contract means you have no financial obligation to the company, but you may still end up losing your bonus if you break it.

At least that’s my understanding