Senior is typically one or two promotions above the entry level. After that the titles resemble something like this:
Staff
Senior Staff
Principal
Senior Principal
Distinguished
Fellow
Staff
Senior Staff
Principal
Senior Principal
Distinguished
Fellow
At best, somebody might have a "tech lead" title but it's not what people hire for.
_Typically_, companies hire for grad, junior, software engineer and senior software engineer.
Maybe principal once in a blue moon.