After 3.Nc3 dxe4 4.Nxe4 the centre is half-open. White has a pawn on d4, Black has pawns on c6 and e6. White has more space, but Black's structure has no weaknesses and every black piece has a good square. Black's main break is ...c5, attacking d4; sometimes ...e5 is possible too.
In the Advance Variation (3.e5) the structure resembles the French: White pawns on d4 and e5 against Black pawns on c6 (later c5), d5 and e6. The difference is that Black's light-squared bishop is already outside the chain on f5. Black attacks the base of White's chain with ...c5.
The Exchange Variation (3.exd5 cxd5) gives a symmetrical, half-open structure in which White often plays c3, Bd3, Bf4 and Qb3 to pressure b7. The Panov-Botvinnik (4.c4) gives White an isolated queen's pawn after a later exchange on d5, with the usual plans: White attacks, Black blockades d5 and trades pieces.
Black usually castles short, but in the Classical, with White's pawn on h5 and the king on c1, Black sometimes castles long instead. Look at the pawn storms that follow before deciding.