moguls are the bumps created in snow with small spaces to navigate in between. here's a picture of a compeition freestyle course. Skiers have to race down the mogul field, and go off a jump (and do a trick), they land and then imediately enter the moguls again, which will lead to another jump, where the vast majority of skiers will do a trick of greater difficulty than the first jump. Then they ski down the rest of the mogul field. They are scored on speed, and tecnique in the moguls and on their jumps. here's a picture of a competition freestyle course. Notice the bumps in the course, those are moguls. On a regular ski hill run they'd be spaced much more sporatically, and they'd vary in size.
a slopestyle course is a competition course consisting of terrain park features. There are major slopestyle comps for both skiing and snowboarding, but so far neither are an olympic event (only half pipe for snowboarding).
A mute grab (for skiers anyways) is when you reach down and grab your ski in front of the toe piece of your bindings, but not the tip, that's a different grab. If you spin
left, you'd grab your
left ski with your
right hand. If you spin
right grab your
right ski with your
left hand.
Now, there's also reverse/leading/opposite mute grabs. They differ from a regular mute grab in that if you were spinning
left you would grab your
right ski with your
left hand, so so the grab is done with the leading hand in the rotation, the opposite or reverse of a regular mute.
also, if you grab further up the front of the ski, it's called a critical. If you grab the actual tip of the ski, then it's a nose grab.