I would say that N+1 is the same as pushing the film 1 stop. However, you will find "pushing" and "pulling" used for either exposure or development changes, or both. The Zone System, in its many forms, is more precise as to what constitutes a normal negative, or the deviations from normal.(posted 8265 days ago)N+1 results in the increase of density of a Zone VII exposure to match the density of a NORMALLY processed Zone VIII. This is accomplished by increased development time. (Although you may have to compensate for the slight increase in Zone I density by a slight decrease in exposure, as I said in the first answer.)
N-1 is accomplished by reducing development time to the point where the density of a negative exposed for Zone IX is lowered to match a NORMALLY processed Zone VIII. (And you may have to slightly increase the initial exposure to counteract the slight lowering of Zone I density)
Other Zones react to the change in development, of course. Lower densities react less and higher densities react more. If you expose a scene that contains a full range of light values and develop it for N+1, Zone VII will go to Zone VIII, by definition. Zone V will be somewhere between a normal V and VI. If the scene contained Zone VIII values to begin with, they will now be higher than Zone IX, because they were denser than Zone VII to begin with, and they react even more than Zone VII to the increased development.