This varies wildly by company, and dynamics of the org/team. The best summary I’ve found is the staff/principal engineer archetypes article[1] by Will Larson. He identified 4 archetypes: Team Leader, Architect, Solver and Right Hand. This categorisation broadly matches my own observations & experience at Uber - even if the formal, internal company definition does not put these as such.

This comes after he interviewed close to a dozen staff/principal engineers at various companies of the likes of Stripe, Mailchimp, Fastly, Slack, Split and others. The stories/interviews[2] are worth reading to get a better picture of exactly what staff/principal looks at each of these companies.

[1] https://lethain.com/staff-engineer-archetypes/

[2] https://staffeng.com/stories