To be honest, not really..I'm sure someone would say the pirc but it's completely different
is there an opening as black vs 1. e4 with similar themes as KIA / KID

Maybe you can still play the KID, but just change the move order to delay Nf6 until the e5 square is secured. Black is accepting a temporary space disadvantage in the KID anyway. And perhaps because White has not played an early c4, Black can look to break up White's center on the queenside with c5 and get some space and counterplay there instead of typically playing on the kingside.

To quote GM Finegold when a student asked him if the kings indian was like the Dragon in any way: "it's like the dragon because it's being played on a chessboard."
maybe accelerated dragon, if white plays some maroczy bind setup.
How would that be similar to a KID?

Some variations of the Ruy Lopez can lead to similar pawn structures as some variations of the KID - that's about it, really.

Closest thing you'll get to he King's Indian Defense is the French Defense. Both often lead to blocked positions as shown below. However, same strategy doesn't mean same attack. The theory of "pawn pointing" applies to both lines below, as it always should in a blocked position, but notice how they are pointing in opposite directions. In the KID - Classical Variation (first diagram), note that Black's pawn point toward the Kingside and White's the Queenside, and note how each normally attack said side. In the line of the French McCutcheon shown below, notice how you also have a blocked center, but also note that the pawns point in the opposite direction, and so White attacks Kingside and Black Queenside. I normally tell students that play the French, asking for a QP defense, to play the King's Indian and vice versa:
King's Indian:
French:
This is a perfect example of how the same pawn structure doesn't lead to the same strategy (i.e. Caro-Kann and Slav are not the same, Pirc and King's Indian are not the same, French and QGD are not the same). Instead, you should focus on openings that lead to the same strategy type rather than the same pawn structure. The French and King's Indian Defense fit together like hand in glove!
ThrillerFan wrote:
The French and King's Indian Defense fit together like hand in glove!
Thanks, I'll look into the French. I've always been a Sicilian Accelerated Dragon player but I find the closed centre positions with races on opposing wings arising from the KIA / KID are far more enjoyable and easier to play for me

Problem with e4 leading to a KID is that usually if white plays e4, you won't see c4 after you start playing in a KID fashion. Instead you will end up in a pirc which is hard to play for black, although I play it myself. Once you don't cry at the sight of the 150 attack, your pirc life will get easier.

By the way, Etherii, in case you are curious which other openings tend to mesh well together, and what I usually recommend to people that play one of the "big 4" against 1.e4 (namely 1...e5, 1...c5, 1...e6, or 1...c6), I usually recommend the following:
French players I recommend the King's Indian Defense
Sicilian players I recommend the Grunfeld Defense
Caro-Kann players I recommend the Nimzo-Indian Defense
Double King Pawn players I recommend 1...d5.
Note that in the case of the last one, a lot depends on which double king pawn defense they play drives which 1...d5 lines I recommend. For example, those that play agressive lines of the Ruy Lopez, like the Schliemann, Bird's Defense, the Moller, etc, I suggest the Semi-Slav. Those that play the Closed Ruy, or the Berlin, I recommend the Slav. Those that play the Petroff instead of 1...Nc6, I recommend one of the 2...e6 lines, like the Lasker, Tartakower, or Orthodox, or else the QGA.
Note in all cases, there is flexibility. Just like how a 1...d5 and 2...e6 player can play the Lasker, Tartakower, Orthodox, or QGA, a Nimzo-Indian player can play the ...c5 lines, the ...b6 lines, or the ...O-O lines, a KID player can play the ...Na6, ...Nc6, or ...Nbd7 lines, etc.
So do note that the openings I pair together are at the 10,000 foot level, and the variations within each opening depend on specific variations of what you play against 1.e4. A Najdorf Poisoned Pawn player might play the lines of the Grunfeld where Black tries to grab the a2-pawn and get away with it while a Taimanov player might go for safer waters with ...b6.
I've bee learning the kings indian attack as White and the kings indian defence as black vs 1. D4 and 1. C4 as they make my opening prep and knowledge of key themes easier to learn.
Are there any setups against 1. E4 that share similar themes / motifs / manouvres as the kings indian attack and defence?
Thanks