The website stats do separate them here:
http://en.lichess.org/people/stats----
HOWEVER,
A draw is when neither side will win.
Just about every single website will have it the same way as lichess.
A draw and stalemate both result in the same amount of rating points being given.
Please read:
"For the most part, a draw occurs when it appears that neither side will win. Draws are codified by various rules of chess including stalemate (when the player to move has no legal move and is not in
check), threefold repetition (when the same position occurs three times with the same player to move), and the fifty-move rule (when the last fifty successive moves made by both players contain no
capture or pawn move). A draw also occurs when neither player has sufficient material to checkmate the opponent or when no sequence of legal moves can lead to checkmate."
From:
http://en.wikipedia.org/wiki/Draw_%28chess%29