So basically
Parallel worlds are just the broad term for all timelines
Adjacent worlds are those close to each other and share many similarities with each other like the Fate timelines but those like the tsukihime, tsuki and notes timelines cant be called an adjacent world to the fate ones
Pruning is when a timeline has no hope of generating any possibilities because its either too peaceful or chaotic. So it has nothing to do with branching too far from the others. Jumping between adjacent worlds. Isnt 2nd magic required to do this?
Quantum timelocks are like the shared events between 2 or more timelines. It doesnt necessarily have to be a perferct copy with each other just the general events. If i remember right the plot of FGO by goetia was to change those timelocks so does that mean that if he had succeded he could have changed the whole nasuverse or at least the fate ones? Someone told me that his plot only affects the GO timeline because affecting the whole nasuverse requires the 2nd magic.