A device is a single entity that can be controlled independently to provide services to the grid. For instance, a single battery controlled through an inverter count as one device. Similarly, two stacked batteries that cannot be controlled independently count as one device. On the other hand, two batteries which can receive separate inputs count as two devices.
A program is the construct that utilities created, in other words the VPP, which end-users can participate in to earn money. There are multiple programs across the US, tied with specific utilities or electricity markets, each with their own rules and requirements.
Enrolling is the act of signing up to participate in a VPP program. An enrollment is therefore the relation between a set of devices plus their site, and a program.
When a utility needs power to be provided to the grid, they call an event. It contains a specific set of instructions (a schedule) as well as start and end times.