I think chai latte is correct, it looks as though they are different threads simply because, although the pitch may be similar or the same the different diameters make it appear different.I'm not sure about this, but those threads look like a different size to me as already said. They also look the same pitch, but the steeper helix angle implies a double start thread. It does actually look like that, but can only really be ascertained by examination. It makes sense in the the parts would move apart when the thread was turned. It also complicates things for anyone making one. Certainly not insurmountable, but just more complicated. Any maker would need to examine the whole plane preferably to take sizes and threads off it.
From my point of view, if I have the parts in front of me then replicating them is easy. I don't really need to know anything more.
If it was a case of making a missing part from scratch, then I agree you would want the whole thing to be able to understand how it is supposed to work.