Understanding owner and member roles
Whoever creates an organisation becomes its owner. Every other person who joins that organisation holds the member role. These are the only two roles that exist today — there's no separate billing-only or read-only role yet.
Role and organisation membership are enforced on the server for every request, not just hidden in the interface — a member of one organisation can never see or act on another organisation's data, no matter what.
Inviting teammates into your organisation isn't built yet — today, each account that signs up creates (or is invited into, once that exists) exactly one organisation membership. Multi-person teams are on the roadmap; see What's coming.