The nappy shaped things are likely to be nappies. Find a teddy or doll around newborn size, and try how things fit. Have they got Velcro or poppas? Do they cross over at the front? If not they are likely to just be inserts, if they do cross over and no Velcro or poppas then they will likely need a nippa to hold it together. Some people just put a wrap over, but I would prefer a nippa. These will need a wrap over the top.
If it has a fold out tongue then it is not a pocket nappy. A pocket nappy is just the wrap and liner sewn together, with a hole at the back to stuff a soaker in.
PUL is a fabric that is sometimes used for wraps. An alternative is wool or fleece
AI1 is all in one, which may or may not have a flop out tongue.
AI2 is all in two which is when bits poppa together.
Two part nappy system is when you have an inner soaker nappy or pads, with a wrap over the top.
Boosters can be whatever fabric you want. Best to get a little selection to see what works for you.
I have never done Longies shorties or soakers.