The with e3 is a variation of the Queen's Indian Defense, catalogued as ECO E14. The line runs 1. d4 Nf6 2. Nf3 e6 3. e3 b6 4. Bd3 Bb7 5. Nbd2 c5 6. b3 Be7 7. Bb2 d6 8. O-O O-O 9. c4, reaching the position shown below after 17 half-moves.
White holds the centre with pawns on d4, and one pawn capture is available, so the structure has not settled yet. Development is level at four minor pieces each. It is Black to move after nine moves. Both kings have castled kingside, so play tends to shift to the centre and the opposite flank.
On the Queen's Indian Defense generally: A flexible defense to 1.d4 where Black fianchettoes the queen's bishop to control e4.
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The with e3 goes 1. d4 Nf6 2. Nf3 e6 3. e3 b6 4. Bd3 Bb7 5. Nbd2 c5 6. b3 Be7 7. Bb2 d6 8. O-O O-O 9. c4. It is a variation of the Queen's Indian Defense and is catalogued as ECO E14.
The with e3 is ECO E14. ECO codes group openings by their move order, so nearby codes cover closely related lines of the Queen's Indian Defense.
Stockfish evaluates the position after 1. d4 Nf6 2. Nf3 e6 3. e3 b6 4. Bd3 Bb7 5. Nbd2 c5 6. b3 Be7 7. Bb2 d6 8. O-O O-O 9. c4 at +0.29 at depth 18, which is a slight pull for White, within normal opening margins. Engine evaluation is only a starting point — at club level the practical value of a line is mostly about whether you know its plans better than your opponent does.
White holds the centre with pawns on d4, and one pawn capture is available, so the structure has not settled yet. Development is level at four minor pieces each. It is Black to move. Both kings have castled kingside, so play tends to shift to the centre and the opposite flank.