Well I will do my best to explain it the way I understand it LOL!
LP is the appaloosa gene that causes the characteristics and colors to be expressed.
If the horse is LP/Lp they have anywhere from just characteristics (mottling, sclera, striped hooves) to leopard
If the horse is LP/LP is your fewspots, snowcaps, and some characteristic only horses too
Now the part that is more confusing is that Appaloosas that are leopards/near leopards/fewspots/near fewspots carry the PATN1 gene which is the actual pattern gene. The PATN1 gene is the leopard pattern gene and supposedly have to have at least one parent carrying this to get a leopard. I however have seen several true leopard foals by parents that I would not think to carry that pattern so Im not convinced all is truly known about how that works yet. You can have an entirely SOLID appy bred horse that does not carry LP but is technically a leopard because it carries PATN1 (PATN1 cannot be expressed without LP). This is why so many appy bred solid horses that didnt inherit the appy gene can still throw louder color when crossed on lp carrying horses.
The other pattern genes are not broken down so much at this point as far as I understand and just are referred to as minor patn genes. Blankets, snowcaps, lace blankets, ect.
Some patterns seem to be suppressed too and apparently black and female can suppress color to make a horse look like it carries less pattern than it really does
I think I will stop at that for now and hopefully someone who knows more will jump in with more info and hopefully make sure I wrote all that right LOL!