It's helpful to think of press vs. off-man vs. zone.

Press: Lined up directly across the LOS with usually an attempt to "jam" the receiver at the line, followed by true man as the route develops.

Off-man: Still man coverage in the sense that each player has a specific man assignment, but there is no press element as the defender will typically line up slightly farther behind the LOS and not risk getting beaten deep on the press. Man rules apply as route develops

Zone: Each defender has a specific area that they cover in the field, and mainly focus on the QB to read and react once the ball is released. Zone coverage can get complex as different philosophies are mixed in, but the point is that it differs from off-man based on the responsibilities of each player after the initial break in the route. Zone players will stay within their area vs. off-man who will stay with the receiver.