When team members take direction from both the project and line managers, the type of project manager is usually Heavyweight team leader.
Step-by-step explanation:
The project manager has direct links to and responsibility for the work of all project participants, usually senior managers in the organization, within a heavyweight team structure. The responsive managers are at the same stage or overridden.
They do indeed have expertise, experience and major corporate influence. In addition, these managers primarily influence public opinion working on the development work and directly monitor their work through key staff members of the core teams.
Often, the fundamental teams (their functional working fields) are committed and physically co-located with that heavy weight project leader.