I don't think that's the literal name of the position. This is a common term to refer to a manager with an organization of ~20-40 people, where their direct rep

I don't think that's the literal name of the position. This is a common term to refer to a manager with an organization of ~20-40 people, where their direct reports are primarily managers themselves as opposed to individual engineers. In most large companies this position is still called something like "Senior Manager" as opposed to Director, VP, etc.