The basic answer seems to be: in Europe, you're in school until you finish your MSc, but once you start the PhD you're basically just considered a junior-ranked research professional and paid accordingly, even if your de jure status is "student". In much of the rest of the world, including but not limited to the Anglosphere, the BSc is the terminal degree, a MSc is a consolation prize for failing your PhD, and a person doing a PhD is considered very definitely a student, with the loss of pay, permanence and status that entails.
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The basic answer seems to be: in Europe, you're in school until you finish your MSc, but once you start the PhD you're basically just considered a junior-ranked research professional and paid accordingly, even if your de jure status is "student". In much of the rest of the world, including but not limited to the Anglosphere, the BSc is the terminal degree, a MSc is a consolation prize for failing your PhD, and a person doing a PhD is considered very definitely a student, with the loss of pay, permanence and status that entails.