Is offlining a Service Group the same thing as failing it over? What does offline mean?

No, when you offline a Group you are shutting down all the services in the group, but you are not onlining it anywhere else. Offline for a Group means the services in that group are currently unavailable to any node in the cluster. You can then online the Group at any time on the same node or on another node if you want. A failover is when a Group offlines from one node and immediately tries to online on another.