To clarify: is the distinction between delta-v and change in re velocity that thrust could be applied in any direction, including in the braking direction, so a rocket applying a maneuver of given delta-v could end up with an increased or decreased (or zero) final speed?
If the above distinction is correct, then in general delta-v is not coupled to the physical change in the rocket's velocity. But in the case of a conventional rocket with a fixed thrust vector launching from Earth's surface (as in OP's comment), isn't it perfectly true that delta-v is equivalent to change in velocity (barring air resistance)?
If the above distinction is correct, then in general delta-v is not coupled to the physical change in the rocket's velocity. But in the case of a conventional rocket with a fixed thrust vector launching from Earth's surface (as in OP's comment), isn't it perfectly true that delta-v is equivalent to change in velocity (barring air resistance)?