Not the same thing at all, man. I speak easily in groups, put myself forward in clinical settings, ask for chances to try procedures (even though it's pretty intimidating with the patient watching you expecting that you know what you're doing) and interviews, etc. In class and small group, I am often told that, if anything, I could improve by putting myself forward less so that others who are less comfortable speaking have more opportunity to do so, even if it takes them longer to speak.
In my social life, I am closer to 30 than I am 20 and I have never in my life been on a single date, and it's largely because of a lack of confidence on that front and anxiety that specifically centers around social things. It's not that I haven't been asked, either, or that I haven't wanted to (though somehow the people you'd actually want to date never seem to be the ones who ask). I'm friendly, outgoing, keep myself in relatively good shape, and I'm good at the things I choose to do. I'm just...not good at figuring out the whole dating thing. I will strike up a conversation and get to know people no problem, it just gets weird as soon as either person expresses a romantic interest. I just don't have the courage to pursue it. Heck, half the time I don't have the courage to acknowledge it openly enough to shut them down, either, so I just avoid the hell out of anyone who's obviously interested.
So, no...you can't equate confidence in academic and professional settings with confidence when it comes to dating. They're vastly different experiences, and you can be on opposite extremes with each (though obviously it would be better to be less extreme on all counts).