Kings gambit for white I'm just a beginner at chess and am just starting to get into the king's gambit but there seems not to be much information on this line probably because I'm not very good and the same with my opposition. I'm used to this line

[FEN ""]
1. e4 e5
2. f4 exf4
3. Nf3 g5


and so on but recently I have been running into this

 [FEN ""]
1. e4 e5
2. f4 exf4
3. Nf3 Nc6


I have run through this on Stockfish but I'm curious if anyone could explain the theory behind the next move.
I remember reading about it in an old Chessbase Magazine edition (circa 2010 I believe). They examined a game where White played Bb5 at the right time, pinning the Knight then later exchanging it for weak queenside pawns, kinda like in the Ruy Lopez. I've used this idea fairly often, at least it's another option to Bc4, the normal development move that might later run into ...Be6 in this case, and it's not like exchanging and playing on the queenside is forced then.

If Black also develops their f8 Bishop, c3 and b4 also take space on the queenside, threatens b5 to kick the c6 Knight, and restrict both the Bishop and the Knight's activity.

In any case, there's nothing wrong with taking the center with 4.d4. As the f1 Bishop might want to go to b5 later, the first question to answer is how should the queenside be developed? c3 reinforces d4 and allows a Qb3-Bc4 battery, but Nc3 brings the Knight to a more active position (controls d5 in particular) than Nd2 where it would block the c1 Bishop. Take back the pawn with Bxf4 at some point (if ...g5, h4), and at this point, it should be clear where your light-squared Bishop can or should go.

At that point, White has completed development and has the center, whereas Black has trouble finding active play for his pieces. White should have a slight, lasting advantage, which should be converted in the long term. The rest is up to what themes you want to play around, but keep in mind the Bb5 idea.