In general, I would interpret "senior researcher" as somebody who has a permanent (or potentially permanent, such as tenure track) position doing research at a research institution. It excludes graduate students, post-docs, people with purely teaching positions, etc.
However, if you are applying for a specific position, I would add one additional criterion for what counts as a "senior researcher." Your letter writer should themself hold a position at least roughly as advanced as the position you are applying for. The people reviewing your application want the person writing the letter should be familiar with the hiring standards and criteria for positions at that level. So while it may make sense for an assistant professor to write a letter for you if you are applying for an entry-level tenure track position, you would want a full professor (or equivalent) to write you a recommendation if you are applying to a senior-level tenured position.