Yes, this. Principal means something vastly different between Microsoft and Google (where at Microsoft it means “Staff”). I even got recruiting emails from some not-popular SV firms for “Principal software engineer” when I had 3 years of experience.
One company out there 'staff' is entry level. Whereas in all the companies I worked at 'staff' was a very prized title to have. Another company I worked at my title was basically just some random bits of roman numerals and something that sounded vaguely like a engineer. I usually just put sr software engineer/developer depending on the company and role.
I "normalize" my previous titles to whatever pattern/scheme my current company uses. It more clearly demonstrates the career progression on your resume and you typically only get a reference check at your previous employer so putting an "inaccurate" title for jobs older than that is unlikely to matter. Obviously don't inflate the titles.