With two notable (and arguably rather important) exceptions, the Trail keeps close to the Wall, except where access problems have dictated detours.
The first exception is the stretch from Wallsend to Heddon-on-the-Wall (approximately Milecastles 0 to 12) where the Trail prefers a riverside route, clearly more picturesque and designed to appeal to those who want to walk another National Trail, rather than pander to murophiliacs. Following this route, however, awkwardly (and embarrassingly) means some rather important and quite famous preserved sections of Wall are omitted.
The second exception is where the Trail again favours a riverine route whilst passing through Carlisle and its eastern outskirts, thereby missing out further visible sections of Wall and its components, including the (admittedly sparse) remains of Stanwix fort.
Further reading: Burton 2003