I have also struggled with some of the nuances around these. I am in a platform engineering org. We have two pillars, SRE and DPE, and our product side has about 250 engineers.
We do not own processes in the PE domain. That would be the things @Steve Fenton mentioned: Getting Things Done, Personal Kanban, or the Pomodoro Technique, or tanyting surrounding the SDLC. We don't currently branch out of the Engineering bit in DPE.
My team owns all the environments up to prod (including deployments), CI/CD, IaC & par, automation, tooling, IDP, and self-service. We play SRE in these spaces as well, so there is a lot of monitoring, quality drivers, and optimizations. We are planning to offer ancillary services for groups outside of engineering soon.
SRE owns production, though we have some shared responsibility, mostly as a holdover from an old org structure.
I would love to also have the
I would note that I am at a high-growth start-up (150-1500 in three years) and joined to drive DPE as a function. The company's engineering org is maturing in many ways, and we're trying to build this function into the company in the 'We need to have appropriate processes, tooling, and standards in place for scaleable growth" stage.