Do we know what exactly defines the AP cost of a weapon? I first thought its fire rate, but this isnt true as i have guns with a higher fire rate such as laster pistols that have higher ap costs than combat rifles...also pistols vs rifles or weight seems only partially true as a 44 pistol for example has a quite high ap cost despite being light and a pistol.... my 10mm despite being modded beyond belief and being quite heavy lets me use an inse amount of shots in vats...?

Another question i have is what defines if a weapon is considered a pistol or a rifle? I assume its mostly the grip used as for many weapons this changes the definition on the item screen - BUT, is this also true for unique weapons? For example if i take a certain unique laser rifle i get from a certain mission which has a unique bonus and a unique name and exchange the full stock for a pistol grip, is it now a pistol?

Yes it is now a pistol.

The pistol/rifle thing is quite hard defined, if it has a pistol grip it uses the pistol perk, it has a stock it uses the rifleman perk, no if or but.

or you can just count your hands

if you see one hand its a pistol if you see no hands its a rifle

Things I found through exponentiation:

The type of the weapon changes if the name changes. For pipe weapons or most energy weapons, it will be very clear. Put a pistol grip, it's a pistol, thus gets bonuses from Gunslinger, put a rifle stock, the name changes to rifle, thus Rifleman. Similarly, the receiver can change most weapons to automatic. Even if they are pistols, they still only get bonuses from the Commando skills if they have "auto" in the name. The Automatic overrides everything. Note that legendary two shot weapons are not considered automatics if they dont have an auto reciever. Sadly, you can't turn a shotgun into a pistol.

In VATS, pistols cost less, and then rifles, and then automatics are most expensive. However, other mods dramatically increase/decrease costs.

The sights are the most obvious. If you add reflex sights, the VAT cost goes down. If you add sniper scopes of any kind, the cost increases.

For the other mods, generally the heavier the mod, the more the VAT cost increases, though this is not really 100%. A drum magazine will increase the VATS cost always, but sometimes the long magazine will not. Some receivers and barrels that are light will decrease the cost, some will increase it. It's safest to save before you mod, and then try the weapon out on a settler, to see how many shots you get out a full vats bar.

Also note that VATS accuracy is apparently sighted aiming accuracy, not hip fire. So while scopes mean less vats shots, they mean a lot higher accuracy in VATS.

Recoil does not seem to affect VATS as far as I can tell, though. Maybe someone has seen a connection? Focus does, so when a mod talks about focus, it means VAT cost.