The with c6 and Nbd7 is a variation of the Catalan, Closed Variation, catalogued as ECO E06. The line runs 1. d4 Nf6 2. c4 e6 3. g3 d5 4. Bg2 Be7 5. Nf3 O-O 6. O-O c6 7. Qc2 Nbd7, reaching the position shown below after 14 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 two minor pieces each. It is White to move after seven moves. Both kings have castled kingside, so play tends to shift to the centre and the opposite flank.
On the Catalan, Closed Variation generally: Black keeps the pawn structure closed with ...Be7 instead of capturing on c4. A solid positional approach where both sides maneuver carefully.
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The with c6 and Nbd7 goes 1. d4 Nf6 2. c4 e6 3. g3 d5 4. Bg2 Be7 5. Nf3 O-O 6. O-O c6 7. Qc2 Nbd7. It is a variation of the Catalan, Closed Variation and is catalogued as ECO E06.
The with c6 and Nbd7 is ECO E06. ECO codes group openings by their move order, so nearby codes cover closely related lines of the Catalan, Closed Variation.
Stockfish evaluates the position after 1. d4 Nf6 2. c4 e6 3. g3 d5 4. Bg2 Be7 5. Nf3 O-O 6. O-O c6 7. Qc2 Nbd7 at +0.49 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.
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 two minor pieces each. It is White to move. Both kings have castled kingside, so play tends to shift to the centre and the opposite flank.