Is the longitudinal stability achieved the same for all aircrafts or does it differ?
Different types of aircraft do have differing requirements for longitudinal stability:
A dogfighter or aerobatic sportster needs to be minimally stable, even a little unstable, for maximum manoeuvrability. On the other hand a primary trainer must be stable, so the novice pilot finds it easy to fly.
Whether the plane is fly-by-wire also makes a difference; relaxing the stability reduces drag and therefore improves fuel efficiency, but it needs a computer to add artificial stability so the pilot does not get tired wrestling with the controls for hours on end.
Technically, longitudinal stability is determined by the position of the centre of gravity relative to the aerodynamic centre. If the CG is in front then the plane is stable, if behind then unstable. The designer has to be careful to attach the wings in the right place for the particular characteristics required.
Some planes can vary significantly in flight. The de Havilland DH.88 Comet racer had a big fuel tank in the nose. When full of fuel it was just stable, but as it emptied during a long flight the CG moved progressively aft and it became more and more unstable (and the pilot became more and more exhausted!).