The relationship between yanas and sects is easy to understand by analogy with the automobile business. A yana is category of vehicle, like SUVs. A sect (or Buddhist “school”) is a brand, like Ford.
Christianity does not have yanas. It does have sects: Catholic, Baptist, Mennonite. So when Westerners first started trying to understand Buddhism, they assumed Buddhist yanas were sects. Mostly this confusion has persisted, and even many scholars still get this wrong.