Certainly vs definitely

Hi, I'm trying to find the difference(s) between 'certainly' and 'definitely'.
Is there any difference when you use them in the below sentences?

• He is definitely in town. I saw him this morning.
• He is certainly in town. I saw him this morning.

I have been told that 'certainly' is objective (based on a fact) and 'definitely' is subjective and informal. Is this true?