This is entirely it. Titles should be consistently ordered within an organization, but they are not portable from one organization to another.
This is a lesson I’ve had to explain over and over to people at the beginning of their careers. I’ve been asked for advice about which offer to take from people thinking about leaving 10s of thousands of dollars on the table because another company will give them a Senior Engineer title and they think that’s important.
When hiring, titles are basically ignored unless the person is coming from a company like Microsoft or Google where their leveling system is publicly known.
I’ve interviewed so many “Prinicpal Staff Engineers” or even “CTO” people who would barely qualify as senior engineers at an average company. I’ve also interviewed “Senior Software Engineers” who had more experience than knowledge than anyone on our teams (and that’s saying a lot!)
Hiring managers know this, but it’s not obvious if you haven’t done a lot of hiring or worked at a lot of different companies.