Short Japanese Culture Questions

What exactly is バイト after all? I thought I understood the term as a part-time job, or temporary job for extra income, as you would do as a student. However, in the book I’m reading, a character is criticized for still doing バイト after many years, instead of finding a proper job. She’s working at the same place though, not doing odd jobs here and there, and seems to be doing full shifts, so I wouldn’t call it part-time either. Is the difference the “permanence” of the position? The income level? The fact that it needs no special qualifications? And is it not considered appropriate for older people to be fully employed in shops/konbinis/etc long term?

As an extra example, in a series I was watching recently, someone working at a hairdressers’ in his 30s was mistaken for the manager by a customer, just because of his age. The dialogue went something like this:
-Wow, I’m getting my hair shampooed by the manager!
-I’m not the manager.
-Oh, sorry, you looked like you were in your thirties.
-Yes, I’m 36.
-(embarrassed silence)

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