Agree to vs. agree on

Still another confusing verb+preposition pair.

A.) He agreed to the new conditions.
B.) We agreed on the price.

When can we use ‘agree to’ ? When can the phrase ‘agree on’ be more appropriate? Please enlighten me.

Well,

I suppose the result in both cases is the same but the methods to achieve it might be slightly different. If one party makes a proposal which is accepted by another party, the second party [color=blue]agrees to the proposal.
If both parties are equally involved in a negotiation process and they finally reach a consensus they [color=blue]agree on something.
Please, note this construction too:
agree [color=blue]to + verb
For example: She agreed [color=blue]to work overtime again. [YSaerTTEW443543]

TOEFL listening lectures: Which is a characteristic of realistic landscape paintings?[YSaerTTEW443543]

Thanks for pointing out this subtle difference.