DevOps is the discipline of being involved in both development and deployment.
Full-stack is when you work on everything in the stack from the database to javascript.
They are two different axis. Ops to Dev:
- Ops provision, set up, and maintain servers but don’t write application code.
- Devs write the application code but do not think much about what it runs on.
- DevOps is the mix of the two.
Frontend vs Backend developer:
- The front end is UI which may be JavaScript.
- The back end is database and business logic.
- Fullstack developers do both.
You could have a Full-stack DevOps but that would be a bit nuts as they would have such a broad remit it would be practically impossible to be good enough at everything.