There's one license, not two. Every state licenses real estate salespeople (and, at a higher level, brokers), and that single license lets you represent a buyer, a seller, or in some cases both. "Buyer's agent" describes who you're working for on a given deal, and that gets set by a written representation agreement, not by the license itself. Same person can list a house on Monday and represent a buyer on Wednesday.
Realtor means a member of the National Association of Realtors, a private trade group with its own code of ethics and its own dues. It's a trademark. Plenty of licensed agents aren't members, and being a member isn't a separate qualification to practice.
Dual agency is one licensee representing both sides of the same transaction. Whether it's permitted, and what disclosure it requires, is set state by state, and a few states prohibit it outright, so your friend's arrangement may be perfectly normal where she lives and illegal a state away. A related term you'll hear used loosely is designated agency, where two different agents inside the same brokerage take the two sides. People say "dual agency" for that too, which muddies things.
The part worth knowing before you tour anything: since the NAR settlement rules took effect on August 17, 2024, a buyer signs a written agreement with their agent before being shown a home, and that document spells out what the agent is paid. Read the payment section slowly. It's the whole relationship in one paragraph.