Don't know why c1 and b1 were both marked as valid spaces, but you are correct that the K moves 2 squares. This from chess.com's Rules and Basics:
Notice that when you castle one direction the king is closer to the side of the board. That is called castling "kingside". Castling to the other side, through where the queen sat, is called castling "queenside". Regardless of which side, the king always moves only two squares when castling.
Hey all, so I was playing a game of daily chess, about to castle my white king queenside (O-O-O), when I noticed that *both* c1 and b1 were marked as valid squares for my king to castle to! I've never seen this before -- can anyone explain this 'three space move' to b1 (and presumably the rook ends up on c1, but who knows?) that the program was prepared to allow me? My understanding was that when white castles queenside the king ends up on c1 and the rook on d1.