This is not now I use these terms, but I’m glad you said this because I think this will help clarify. In order to understand what I mean when I use these terms, you have to look at this at three levels:
Body mechanics. What you are describing are obviously different physical movements. One involves only wrist. Another involves some forearm. Done.
Type of pickstroke. These are both fully escaped pickstrokes. These two movements are the same at this level, and the picking pathway when viewed under a camera looks similar, regardless of whether forearm is involved or not. The motion appears curved because the pickstroke is escaped at both ends.
Alternate picking style. This is perhaps where I’m confusing people. Levels 1 and 2 are enough to describe anyone’s playing style at the level of the movements. You can look at every pickstroke a person makes, and decide which physical mechanic it is, and whether or not it escapes. But what about when you notice that certain patterns of usage repeat between different players? In other words, what do you do when you notice that certain players use similar combinations of physical movements and pickstroke types? That’s when we need a third, higher-level category: the picking style.
For example, if we see a player who only ever uses single-escaped pickstrokes, that’s one usage pattern: one-way pickslanting. If we see a player who mixes both types of pickstrokes, the single-escape and the full escape, that’s a second usage pattern: two-way pickslanting. And if we see a player who uses only fully-escaped pickstrokes, that’s a third usage pattern: crosspicking. It doesn’t matter what the body mechanics are. Forearm rotation is not “crosspicking”. The habitual use of fully escaped pickstrokes is “crosspicking”, no matter the body mechanic type.
It doesn’t matter that the physical motions involved feel different. That is only reasonable - they are different physical movements. What we are talking about here is taxonomy, how to organize players by what they have in common. And these commonalities aren’t always obvious. Again, someone like Andy Wood is a great example. When viewed at the level of the movements he makes, it seems like a jumble. He uses forearm sometimes, and other times he does not. But when viewed at the level of the pickstrokes, he is clearly a two-way pickslanter, because he mixes the two types of pickstrokes when playing fast. He is distinct from players like Carl Miner because he does not have the tendency to make fully-escaped pickstrokes all the time at those speeds.
However, Andy does have a crosspicking ‘mode’ where he does this. And it’s something he does at moderate speed on both guitar and mandolin. It’s supinated, with full range of motion deviation and extension below the string. It is mostly wrist, but you’ll see bits of forearm here and there, on some string changes more so than others, depending on lots of relatively minor variables like what string he’s playing on and so forth. So if you try and use the presence of forearm movement to determine whether he is “crosspicking” or “two-way pickslanting”, you will be very confused. But in all cases, when Andy plays this way, the pickstrokes fully escape. So the only category that makes any sense is the higher-level usage pattern: crosspicking.
We could, if you like, create other higher-level usage patterns. In fact, we already have. We have “primary” two-way pickslanting, which refers to a particular combination of single- and fully-escaped pickstrokes. We even have subcategories there, like “primary up” and “primary down”, which refers to specific body mechanics and pickstroke type combinations. These categories are useful to have because we notice there are lots of players that fit it, and it helps you recognize them when you see them. It also helps you make guesses as to why a particular player may use or have chosen these particular “recipes”, and that in turn feeds back into your understanding of how the movements work.
You may notice other similarities in usage patterns over time that are worth naming, to help you recognize them when you see them. The “parallel extension” two-way pickslanter would be another such category. But as you point out, it’s not clear that anyone actually plays this way. So it may not exist. But positing its existence is a useful thought experiment and who knows, maybe it exists. If it does not, maybe we’ll understand why.
But if you keep looking at the forearm and trying to determine that way, you’re going to run out of options because by itself, forearm movement or no forearm movement, or wrist extension or no wrist extension, they are just movements. The are the lowest level of the hierarchy, and not enough to describe all the meaningful patterns we’re observing.