My terminology is really limited to the art I’m studying, but I have a feeling that we also do the inward-outward elbow combo you’re talking about.
By title, the elbows I mostly use are:
Crashing elbow(which is downward, but from up high, you bring your arm back as if you are chambering your fist, but you continue so that the elbow comes all the way up and crashes down)
2 techs using crashing elbow
-squared off with your opponent, your right side forward, with your right hand grab just above the opponent’s left elbow, pivot your lead foot back at the same time you do a crashing elbow. This should pull him headfirst into the elbow.
-when in very close range, left leg forward, press the opponent forward at the chin or chest with your right hand, bring your rear foot behind your opponent’s lead leg(well inside his stance), at the same time releasing your right hand from his chest and doing the crashing elbow with your left elbow. This should cause him to be bringing his upper body back up(from being pressed by your right hand and his root messed with by your formerly rear leg) just as the elbow hits his chest/collarbone.
Collapsing Elbow(basically, if you held your elbow out to your side like you just elbow jabbed someone to the ribs, then circled the point of your elbow in a circle that was parallel to the ground, until it occupied your centerline, except the are itself does little of the elbow, it is almost all waist).
Techs with collapsing elbow:
-grab the opponent’s lead wrist, pivot your rear foot until its behind your opponent’s lead foot, and elbow to the kidney area.
-in very close range, you can do this elbow a lot, especially if the opponent is trying to crowd you.
Upward elbow(to my knowledge, same as in other arts)
“elbow jab”(not sure the name, a simple one, just like “ribbing” except once the student gets the related chi kung, he can implement a particularly nasty jing). It’s use is pretty simple, I’m sure everyone here has used it.
Whoever mentioned the problem with getting close above, my recommendation is to assess whether you are holding back too much. Try aggression, not as in anger, but just make a practice sometimes to just go in no matter what. You’ll get pasted sometimes, but if your goal is to get inside, like me(my art works well inside), you won’t really see what prevents you from getting in until you go there.