Both draws and stalemates give each player 1/2 point. There are a number of ways a draw can happen. (By agreement, insufficient material, three position repetition, 50-move rule, etc.) A stalemate is one particular type of draw, in which the player on move has no possible legal move and his king is not in check.
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Originally posted by SavateNo, it wouldn't. If you and your opponent are both down to a king and two pawns, but one of his is about to promote and yours are not, it's very probably not a draw but a win for him. If you are both down to a king and two pawns, but he blunders, you may be able to win. If you're both down to a king and two pawns, and you both play reasonably well, then it will be a draw.
So if you and your opponent or both down to a King and two pawns, that would be a DRAW or a STALEMATE?
I'm just trying to learn how to identify the difference...
You can reach this draw in two ways. You can either muddle on, occasionally shoving pawns forward or exchanging them as it happens, until you reach a situation where you have either only the two kings left, or you have made 50 moves without either of you moving or taking a pawn; or you can decide to end it there and then and make it a draw by agreement. I advise the latter way of action, since it saves a lot of needless woodpushing; but do note that it is up to you both to agree to this draw. King plus two pawns on both sides is not an automatic draw.
A stalemate, OTOH, is an automatic draw, but it's a specific kind of draw. It is reached when one player must move, but cannot make a legal move, yet is not in check right now. It is probably possible in theory to achieve stalemate with a king and two pawns each, but usually it would be rather hard to do so without active assistance from your opponent.
You want to read http://www.fide.com/official/handbook.asp?level=EE101 , in particularly section 5.2; and note point a. in that section.
Richard