You can shoot all the games - with any gun you want ! I did that, for many years with a fairly standard filed grade Browning 12ga, BPS, pump gun with a 28" barrel and screw in chokes.
As I matured in the games ...I got better when I went to a heavier and longer gun for "Trap". I have a single barrel break open Trap gun ( Browning BT-100 / forerunner of the current BT-99 model) in a 34" barrel ..but it isn't my favorite gun. My favorite Trap gun is a Browning O/U Citori XT with 32" barrels and gross weight of about 10 lbs. I like a Trap gun to shoot a 70%/30% pattern over the Point of Impact or maybe a 60%/40% ...so I can float the bird above the rib a little. I like a heavier gun / because it absorbs more recoil - and because since in Trap / there is less left to right barrel movement than the other games ..a heavier gun is an advantage / it maintains its momentum - and stays smooth thru on follow-thru. I shot 25's with my Browning pump ...but I never shot 100 straight ...and the Citori XT's let me get to that level - once in a while ...
On all of the other games / personally I go to a Browning Citori O/U XS Skeet model with 30" barrels and gross weight of around 8 lbs. The 8lb gun /and shorter gun ...allows me to be a little quicker on those hard crossers / where you might get more left and then one to the right ( like on a Skeet field). But I use that same gun for upland bird hunting, for Skeet and for Sporting clays and 5 Stand. To me - that style of gun is a good "all around gun" ...does a lot of things well. I'll never master Skeet - in 12ga, 20ga, 28ga or let alone in the .410 ...and the 100 straight is eluding me ..and father time, and poor eyes ...are making it as "slim to none" odds ....but I keep trying ...
A Trap gun ...32" and 10 lbs ...swings like a big ole sewer pipe ...at the faster games like Skeet and sporting or hunting birds like quail, phesant, etc. ...not that it can't be used / but its not optimal, in my view.
But all of this is personal / at 6'5" and 280 lbs or so ..and 60 yrs old ...what works for me / may not work for you. My shooting buddy is 6' or so / mid 60's and 165 lbs ...and his general purpose guns ( skeet, sporting, 5 stand ...are a little heavier than mine / he likes a 10lb gun / and he goes to shorter barrels at 26" ). To him - that's a perfect balance. For Trap he goes to a single barrel break open gun / Krieghoff / KX 5 in a 34" barrel - at around 10lbs as well. He likes his guns for all games at about the same weight / but longer for Trap and specialized ( he likes a 70%/30% pattern or even an 75%/25%)......
Both of us shoot guns with parallel combs --- for all games and for hunting birds.
Marketing depts for gun mfg's ---- have skeet, and sporting, and field, and whatever guns ( Browning has about 28 models of their Citori line of guns ) and I think most of it is nonsense. You have to figure out what "Fits" you - so the guns hit where you look ( not all guns will fit everyone / heck, some guns, from popular mfg's will not fit hardly anyone ...) - but they still sell a lot of them....
For fun / casual shooting -- having some laughs ....shoot whatever you want / within reason of course - that will give you some success. This week - to my buddies - I issued a pump gun challenge at Skeet ( 100 targets, loser among the 3 of us ...buys lunch ) ...and we're arguing right now on how many birds to give eachother to make it even. Its not about lunch or who gets a free coke out of the deal ...its about having a good time and some laughs !! You have to decide where you fit ..on all these trend lines ....