The with e3 is a variation of the Queen's Indian Defense, catalogued as ECO E14. The line runs 1. d4 Nf6 2. Nf3 d5 3. c4 e6 4. e3 b6 5. b3 Bb7 6. Bd3 Nbd7 7. O-O Bd6 8. Bb2 O-O 9. Nbd2, reaching the position shown below after 17 half-moves.
Both sides have pawns in the centre (White on d4, Black on d5), 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 d5 3. c4 e6 4. e3 b6 5. b3 Bb7 6. Bd3 Nbd7 7. O-O Bd6 8. Bb2 O-O 9. Nbd2. 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 d5 3. c4 e6 4. e3 b6 5. b3 Bb7 6. Bd3 Nbd7 7. O-O Bd6 8. Bb2 O-O 9. Nbd2 at +0.08 at depth 18, which is balanced. 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.
Both sides have pawns in the centre (White on d4, Black on d5), 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.