http://stopthecrime.net/COMM%2012%20BRIEFING001%20(1).pdf
What was Mueller before he was appointed? A Special Counsel is an appointed position when an AG recuses themselves.
And Mueller wasn't an SC until he was appointed. Read what you just wrote, you answered your own question.
Step 1: AG Barr recuses himself
Step 2: RR appoints a SC
Code of Federal Regulations : §600.1 Grounds for appointing a Special Counsel