The name of the show was attributable to The Rock in 1999 when it debuted, but the term "smackdown" has since become an accepted word in the American lexicon, even appearing in Merriam-Webster dictionary nowadays, and its definition is applicable to any sort of heated disagreement.
Smackdown! started on Thursday nights amidst the "WWF Attitude" campaign as a 120-minute program on UPN, but it moved to Friday nights in September 2005. After UPN merged with the WB to create The CW and dropped the program (because WWE's audience was not in their target demographic) in 2008, the show was picked up by MyNetworkTV for a couple years before Smackdown found a stable home on SyFy.
In April 2002, World Wrestling Entertainment split its roster into separate brands. Smackdown! has always been known as the "blue brand." These days, Friday Night Smackdown is the preferred show of fans that want to watch for solid wrestling action whereas Monday Night RAW ("the red brand") is seen more as a variety show, i.e. "sports entertainment."