What are early/inside and late/outside turns (see, e.g., PBN Manual Order 8260.58A) and when do pilots perform them?
I think what you're talking about are what pilots refer to as "fly-past" and "fly-over" waypoints.
Up until recently, all waypoints in the world were "fly-past", ie you could cut the corner from one leg to the next and not actually fly over the waypoint itself. This is still the standard, unless otherwise stated.
But then some SIDs and STARs needed people to actually fly OVER the waypoint before turning onto the next leg, and so coding was included in FMCs etc to get the autopilot to not start the turn until AFTER the waypoint. The difficulty is that there's usually not any differentiation in the presentation on the CDU between "fly-over" and "fly-past" - you have to look at the produced track on the ND to then see whether you're cutting the corner or turning after the waypoint.