You can put it into words however you want, and some people here have given decent definitions (in my opinion), but confidence is a feeling, and also, a lack of feelings as well.
Let's put a hypothetical example: have you ever felt that "fear", "reserved" or "cringe" feeling before doing something, because it felt daunting at some level? Like asking someone out, or doing something that you consider embarrassing, or fighting back someone physically stronger than you?
That's a combination of emotions that I'm not going to get to, but the lack of those, and furthermore, the added one that makes you truly believe you can overcome this, that you'll be OK no matter the outcome because you're strong enough to take it (not just physically, but mentally/emotionally) is how I would describe "confidence". That's what it is, a further explanation would have to describe qualia (which is a waste of time, I should have conveyed my message clear enough).
You have to be careful though, because it could cloud judgement (if you're stupid about it), there needs to be a balance between that, common sense, and proper judging skills. Being smart with this does not take away confidence away from you, it may make you look deceptively hesitant, but that's a price you'll have to pay in order to act in the best way possible (e.g: armed robbers enter the mall you're in, but you letting the police deal with it without risking your life, instead of acting by yourself, which will most likely end up in you getting shot in the guts).
How you achieve this can be done in a myriad of ways, from natural means (getting used to make semi-bold decisions, like making speeches when you have social anxiety, in order to train yourself, or trying being a theatre actor/actress as a hobby), somehow manipulating your mental state (thousands of ways to do it), to "artificial" ways (like people using drugs, being clinically insane, etc).
An example of "artificial" unhealthy volatile confidence (not an official term, but describes it adequately) is the one displayed by Charlie Zelenoff. This guy is a mentally unhealthy, drug addict that will challenge anyone and everyone to boxing matches, regardless of anything. Of course he gets beaten up, enough to even make him run for his life before one minute passes, but that inital boldness of challenging anyone, which is probably caused by his ill mental state and drugs, is an example of retarded confidence. For normal people, not even to this extreme, they'll eventually get their shit pushed in by life itself and lose this feeling (or not if they're lucky), so that's why proper judgement needs to go alongside confidence. To reiterate though, it's a feeling that translates into you very willingly confronting challenge.
I think differentiating between confidence and self-esteem is just being pedantic with semantics, usually unnecessary.
Self-esteem can just be "confidence in one's own worth, abilities, or morals", so that's essentially what you're talking about. However, if you want to write a trivial article about how these 2 things are different, you could just say that a difference would be that one is more general (confidence), and the other is more specific (self-esteem). So, for the latter, you could have the highest amount, yet not be confident about winning a Poker game. Your self-esteem is not challenged, no one would say that, yet you are not confident on something, in this case winning this game.
Barring this example/similar example, you can just use both terms interchangeably.