What makes an opening system different than a standard opening?

Yes! Great question! I haven't seen much written on this subject, so I put in a several hours and tried to catalogue all the opening category "types" of opening names. I mean what makes something an "Opening" versus a "System" versus a "Formation" and so on. Well...there is an answer and I made a roughly 45 min YouTube video on it. The video is simply a list of the various opening types I could think of and I have at least one example of each.

Haven't seen anyone do something exactly like this before, so I was happy with this topic idea.

As a London player myself, I can attest to the fact that a system is basically a set of moves, (although the order could change depending on the opponent's moves) which you can play against many openings. 

Very helpful video you've made. But don't system openings lead to a formation?

Not exactly, something like the KID is a system opening in theory but has hundreds of moves to know and rarely turns out the same every time… similar to playing the Jobava london (system) vs the triangle “formation” in the London (also a system, but could be considered a formation?)

imo, pawn structures dictate formations, piece structures dictate systems

sometimes the pawns are different but the pieces are the same, other times vice versa

Not necessarily. Just like @ninjaswat mentioned below; formations refer to specific pawn formations whereas systems are configurations of pawns and pieces thematic to that setup and can be played against almost anything the opponent plays. 

The London System is a "system" opening, so the white pieces (side opening is for) can play this opening against just about ANY setup (other than maybe 1. d4 e5 Englund Gambit or something xD). Conversely, a formation such as the "hedgehog" formation might actually arise out of several different chess openings.

Now, I realize that common setups like the fianchetto for black against 1. d4 of various Indian Defenses (King's Indian, Old Indian, Pirc etc.) are sometimes thought of as a "system" but this isn't really correct because you can't play the King's Indian Defense against just about ANYTHING. The fianchetto setup in that opening might work against most things, but not the exact series of moves with no regard to what the opponent does...rip @GothamChess xD

So @ninjaswat and you both mentioned that Formations are exclusively made of pawns. It seems like the "All systems have formations but not all formations have a system"? 

Yes and that is just about verbatim to a line I say in that video I posted

Obviously, that sentence has a certain flare of 1st Order Logic thrown in there. The same can also be said of this in relation to Set Theory by John Venn (creator of the Venn Diagram). It is like how all chairs are furniture, yet not all pieces of furniture are chairs.

"Systems" tend to have little to no value placed on moves and move orders beyond named theory. For example, in the London, you can pretty much premove d4 Nf3 Bf4 e3 c3 Nbd2 Bd3 Qc2. If they play 1... e5, switch to the Englund, if they oppose your DSB, drop it to g3 and trade with the h-pawn, if they move Bf5/Bg4 before e6, play c4 instead of c3, but essentially the same thing'll happen in every game until you hit about 1700, when people start playing London prep with Qb6 and keeping their center and bishops flexible.

Idk If I play system openings correctly, but I normally do random moves until i have the pawn pyramid, bd3, nf3 and nd2

Also I prefer 1.d4 2.bf4 3.e3 4.c3 5.nf3 6.bd3 7.nd2

That's what I'm saying. The moves themselves don't matter, and you can pretty much play them in whatever and still get your preferred outcome.

Any concept which is aimed at playing the same moves against any opponent setup is severely flawed by design.

All those "system openings" are NOT made with such an idea in mind. You must  always adapt your move orders, piece and pawn positioning and plans according to the opponent's moves, else you are playing acey-deucey, not chess.

They're all okay except the Caro