Yes -- and no.
SmartNet II is simply a feature set available for Type II trunking systems. Some of the features are esoteric; the most notable is "Priority Monitor," a system that enables a priority function while scanning the trunked system.
SmartZone is a system that involves linking two or more SmartNet "systems," which are now called "zones." In its most general form, SmartZone has two functions of note: a subscriber unit properly programmed for SmartZone operation will select the appropriate "zone" on its own, as the subscriber moves about; and some (but not all talkgroups) will be repeated on a non-native "zone" if a subscriber has affiliated to that "zone" and is selected on that talkgroup.
A SmartZone subscriber unit must be capable of affiliating, which means it must have a valid UserID. A SmartNet radio, however, can listen to all traffic on any SmartZone "zone" except that "zones" must be selected manually.