Join Date: Jun 2005
Location: PBI | Formerly CLT, LHR & AMS (with just a bit of PSP)
Programs: Proud AA CK Spouse, AA Plat, HH Diamond, BonVoy Titanium, Caesars7* (comp), Wynn Black, HR Icon
Posts: 8,208
Not really much of a difference.
It is always listed as FREE for offers, and COMP when you just search without an offer, IIRC.
Of course, you are better off NOT using the offer (unless there is something else with the offer like a gift-card, spa treatment etc.) -- since once you use the offer, you cannot use it again.
Depending on dates, when you are booking, and your overall theoretical there are definitely times when you will get the room "COMP'ed" with an offer, but not "COMP'ed" if you just did a regular search on the same dates.
Also, sometimes the offers are good if you are trying to book more than 2-3 nights. For example, if you plug in 5 nights and only the first 3 come up COMP; you can then call and extend the reservation using the offer for the final 2 nights (at COMP).