Nice posts! I think the Reti Opening: Reti Gambit is recognized as an English by many other databases.
How many variations has Réti made?

1.Nf3 is not the Reti Opening. Another one of chess.com's idiotic mis-namings of openings.
1.Nf3 has no name yet. King's Knight opening, if you have to name it.
By definition, the Reti Opening is 1.Nf3 d5 2.c4. The following, for example, are not Retis:
1.Nf3 c5 2.c4 - English Opening
1.Nf3 Nf6 2.c4 - An English for the moment, but can transpose to a Reti after say, 2...e6 3.g3 d5
1.Nf3 d5 2.g3 - This could transpose if a later c4, but this is not a Reti.
Also, the Reti Gambit is not 1.Nf3 d5 2.c4. There is no "Reti Gambit Declined". It is only considered the Reti Gambit if Black takes with no effort by White to immediately get it back, like 1.Nf3 d5 2.c4 dxc4 3.g3 or 1.Nf3 Nf6 2.c4 e6 3.g3 d5 4.Bg2 dxc4 5.O-O.
Also, the Reti Gambit is a line against the French with 2.b3.

@Yigor thanks for the list the was very helpful though I wouldn't really count all of those funny variations after the Réti Opening because Réti didn't create them. Also how did you find that list?

1.Nf3 is not the Reti Opening. Another one of chess.com's idiotic mis-namings of openings.
1.Nf3 has no name yet. King's Knight opening, if you have to name it.
By definition, the Reti Opening is 1.Nf3 d5 2.c4. The following, for example, are not Retis:
1.Nf3 c5 2.c4 - English Opening
1.Nf3 Nf6 2.c4 - An English for the moment, but can transpose to a Reti after say, 2...e6 3.g3 d5
1.Nf3 d5 2.g3 - This could transpose if a later c4, but this is not a Reti.
Also, the Reti Gambit is not 1.Nf3 d5 2.c4. There is no "Reti Gambit Declined". It is only considered the Reti Gambit if Black takes with no effort by White to immediately get it back, like 1.Nf3 d5 2.c4 dxc4 3.g3 or 1.Nf3 Nf6 2.c4 e6 3.g3 d5 4.Bg2 dxc4 5.O-O.
Also, the Reti Gambit is a line against the French with 2.b3.
What are you talking about?? 1. Nf3 has 2 names. The Réti Opening AND The Zukertort Opening

Thrillerfan is correct.
Thrillerfan said 1. Nf3 has NO name
I meant about the English.
Welcome back everyone to the second forum in the How many variations series! Today we will be looking at all of Réti's opening variations. Here are the ones I know:
Réti Opening:
Réti Opening: Réti Gambit
Tarrasch Defense: Two Knights, Rubinstein, Prague, Réti Variation:
King's Gambit Declined: Classical, Rubinstein, Réti Variation:
Scotch Game: Scotch Gambit, Dubois Réti Defense:
French Defense: Réti-Spielmann Attack:
Ponziani Opening: Réti Variation:
Sicilian Defense: O'Kelly, Réti System:
King's Indian Attack: Symmetrical Defense, Réti-Smyslov Variation:
French Defense: Horowitz, Réti Gambit
King's Gambit Declined: Falkbeer, Réti Variation
Sicilian Defense: Kan, Réti Variation:
Réti Polonaise:
Thanks for reading the second forum in the series of How many variations! Those are all the variations that Réti has created that I know of. The most interesting thing I find is that he has not contributed much to openings like the Ruy Lopez or Sicilian Defense. And lastly, like always please tell me below if you know any other variations that Réti has created or any other interesting opening variations. Thanks For Reading!!