It really depends on what the roles of developer and tester are in your company.
IMO, a tester should be doing nothing that a competent developer hasn't already done, which really makes them a "verifier" that the software works like it should. This is especially true in a waterfall environment.
In an agile/iterative environment, especially one practicing test-driven development (TDD), then the tester plays the verifier role, along with helping with test automation, thinking up test scenarios along with the devs, knowing all the outskirts of the system, and looking at the software like a user and business analyst/product manager. Additionally, they would drive efforts to root cause every single bug and help the team think of ways to never produce a bug like that again.
All of these skills you can get as a dev (and imo you need as a dev), but you don't focus some of them as much, particularly the thinking like the user and BA/PM.
One main difference in mentality is that devs tend to focus on solving a problem with given variables, whereas testers tend to think about how many permutations of the variables you can have. When practicing TDD, the dev is forced to think about that as well, removing the need for that portion of the tester's job (usually). However, that frees up the tester to be a user advocate and identify systemic problems with process, which is a very valuable skillset to have imo. The PM focuses on getting features out of the door, the devs on coding those features to full quality, and the tester on making sure each feature and microdecision makes sense in the bigger scope of things.
In summary, it's not whether your title was "tester" or "dev" it's what you did in those roles that you need on your resume, and those roles vary based on the company/team.