No, courage isn't the absence of fear. If there's no fear there's nothing to be courageous about, is there?
Fear is a very necessary human emotion. Our ancestors would never have survived if they hadn't learned to fear wild animals, for example. It's a good thing to have a sense of fearfulness at times, otherwise we'd go ahead and do things that could mean an end to our very existence.
As for what to do in the face of something that frightens us, that depends on what that something is. Sometimes it's good to face whatever it is, but many times it's good to back away too. Only foolish people would put themselves into danger for no good reason, eg if I saw a lion in my garden I'd be too afraid to approach it. If someone else insisted on going up to it to 'face' it I wouldn't think he was courageous, I'd think he was mad!
IMO having courage is facing and coping with things that devastate our lives, such as serious illness, poverty, breavement. These type of things require sustained courage over a period of time, which must I think be harder than a sudden heroic act on the battlefield which is done in the heat of the moment. Fear and courage are linked, but courage is not the absence of fear - it's a lot more complicated that than.