Drag is aerodynamic force that is parallel to the flow velocity, which has the same direction as the flow velocity.

Lift is the (positive-upward) aerodynamic force that is normal to the flow velocity (perpendicular to the flow velocity). Lift is not drag and drag is not lift.

In the case of a non-rotating cylinder or a fully symmetric airfoil at zero angle of attack (with respect to flow velocity), there is drag without lift. The pressures at the top and bottom surfaces are the same, resulting in no net force. However a body cannot generate lift without generating drag.