When choosing one of these orders as the main ones, one also fixes which operation is considered a meet the one giving the same order and which is considered a join the other one.
Why are they not available?! Instead it comes from the little speaker which is used for normal phone calls.
In other words, the two approaches yield essentially equivalent concepts, a set equipped with both a binary relation and a binary operation, such that each one of these structures determines the other, and fulfill the conditions for partial orders or meets, respectively.