The steering group meeting can also be a gate review meeting, and the steering group can also be the gate review board. Let me explain...
The gate review meeting is a meeting with a specific outcome to decide whether the project can move past the gate or not. The steering group meeting can be any high level meeting about the project (where the participants of this meeting are the steering group members). That meeting might a gate review meeting.
Also, in almost all cases, the gate review board is the same as the steering committee group.
So, in my opinion, your theory is more or less correct...