It's funny how people who treat Judo like a TMA and are focused on technical purity look down on wanting to actually throw people in live situations. Show me examples of matches featuring sasae and hiza where the throwing motions are distinct, where one is a clear wheel and the other is a lift. You're not going to find them, because the throwing motion of both is not that pure in real life. You pull, you lift, you wheel, you block, it's not dependent upon foot placement or specfic gripping situations, it's dependent on what your opponent is giving you and worrying 'I'm going for hiza here, so I must wheel and not lift' is a good way to never throw anyone. You think high level wrestlers worry about whether their single leg is more of a sweep single or a low ankle single? You practice variations, you find a motion that works well for you based on your body type, strength profile, gripping style, etc and you go with it.
I'm not arguing that there aren't different components of throwing motions. I'm arguing that giving them distinct names and trying to draw clear lines between them is unhelpful because those lines blur the minute your opponent starts offering resistance. You should understand the different ways that you can create kuzushi and complete a throw, but you shouldn't mentally separate those methods which is what too much nomenclature causes you to do.