Uhmm no, Captain Marvel was a man by the name of Mar'Vell a Kree Alien, when he died he passed his powers on to Rogue from the X-Men, you are referring to Ms. Marvel and has had over 5 female incarnations with Danvers being the least liked.
You've got it backwards. Carol Danvers was the First Ms Marvel who was with Capitan Marvel when there was an explosion and her DNA was merged. There were three different Ms Marvel (or Mrs) lines published TWO with Carol Danvers. Of the capitan Marvel series there are 5 and The one where Carol Danvers Mrs Marvel takes on the Title of Capitan Marvel is the most recent and she leads the Avengers.
I hope that helped spell it out. I looked it up.