could someone kindly shed some light on the difference therebetween? 

BTW, if i intend to mean TO ARGUE AGAINST THE OPPONENT'S ARGUMENT, which one of the two fit better here. tks

The two terms are similar, but in court, I've seen the term "offer a rebuttal" or a "rebuttal testimony" more often. (just my 2 cents) 

This may be a more accurate distinction: Difference between rebut and refute 

Hope that helps.

Rebut/Refute
In Rebuttal 
By Evan Jenkins

The team was waiting to hear what would happen to sexual-assault accusations against one of its members, the article and headline reported. The bank of the headline said, “No charges yet as teammate refutes woman’s claim.” The accused player hadn’t yet refuted anything; there had been no finding on the truth of the charges. The word is stronger than “rebut,” with which it’s often confused. “Refute” means to disprove, conclusively. “Rebut” means simply to deny, or present argument against, an allegation. And more than half the time, “deny” will get the job done more naturally than “rebut.”

CJR