Why do some ratings change for the opposition - sometimes when i accept a challenge does there appear to be discrepancies with the opponents rating? the rating of them may be say 1451 but their last completed game shows a rating of 1172
People have multiple ratings here. They can have ratings for bullet, blitz, standard, online, chess 960.
When you scroll over a players name, you see only one rating. I believe that chess.com shows the highest rating among the types of chess you are active in.
When you pull up a player's profile and look at a list of the games completed, you see all the games they have played recently- both "online" correspondence type games and live chess- bullet, blitz and standard. Their last complete game may be a blitz game and their blitz rating may be much lower than their online chess rating. (I think that blitz ratings are typically much lower than "online" ratings.)
You haven't played any type of "live" chess here, so you only have a rating for "online" chess displayed.
Why do some ratings change for the opposition - sometimes when i accept a challenge does there appear to be discrepancies with the opponents rating? the rating of them may be say 1451 but their last completed game shows a rating of 1172