Proffer and Offer are two examples of English words that have almost the same meaning. At times, depending on the nature of the sentence you are constructing, both can be used interchangeably. However, the main difference between the two is your ability to know which of the two to use when constructing sentences. This is the more reason why you can't just substitute one for the other.
Proffer has the same meaning as an offer, which is to propose to give something for acceptance or rejection. When you want to give some kind of advice that will help someone manage a particular situation, it usually sounds good to use the word 'proffer' instead of the offer. Also, the offer is usually considered to be appropriate when presenting something to God as a gesture of worship. Using proffer instead of the offer will not give it the right meaning. Invariably, the difference between the two words largely centers on the right word that should be used.