It seems like you're looking for a single group to associate yourself with, yet you are also a member of more than one group. A group of project managers may not directly work together on the same projects, but there can definitely exist a solid camaraderie between all members.
Your fellow project managers may have mentored you or you may have mentored them. Perhaps you bounce ideas off each other when you encounter a PM problem you're stuck on. While you don't succeed or fail together on the same projects, you may definitely have a bond because of your shared problems and similar roles.
At the same time, you also have a bond with the production team. The production team is getting their hands dirty, literally or figuratively, in order to meet the schedule you've given them. Your roles are drastically different, but you all are part of a cross-functional team that succeeds and fails together. While your relationship with the production team may be different than with other PM's, you may still have a strong bond with that group because of your shared goals.
Finally, the stakeholders may be a group you associate with because, in a way, you have a stake in the project as well. Anyone who loves their job or takes it seriously has something to gain from the success of a project. While it's not the same gain that a management-level stakeholder or client may experience, you may share in that experience when a project succeeds. The time you've spent working with stakeholders to ensure your project is successful may bring you closer together just as your time spent with production and PMs brings you closer to them.
Your role as a PM is enhanced by being a part of all of these teams, and to try and segregate yourself into one group or another may alienate the PM team, the production team, or stakeholders. Since you already feel a part of the 3 groups, embrace that! It will help keep you successful.