If you are replacing a uPVC door then yes you would need to replace both the frame and the door leaf as most of the uPVC frames are not interchangeable.
Modern doors help to reduce draughts in your home, so ensuring that it is fitted properly is important. The design of different doors usually means that the locking system is an integral part of the door, so the correct frame needs to be fitted at the same time as the door to ensure that the latch positions are matched.
If you were to fit a new door into an old frame, it might not fit precisely into place, meaning that it would not seal correctly when closed causing unwanted draughts and additional strain on hinges. The door and frame are essentially a single system.
Doors and windows are fitted in the same way, with the frame fastened to the external walls of your home. This means that there will normally be no disturbance of the decoration in your home, and you will not need to paint or wallpaper around your new door once it has been fitted.