The third kind are wandering Samurai, meaning Samurai without a lord.
For all sorts of reasons—like their family going downhill, their previous lord kicking the bucket, or some juicy internal family drama—they can't stay in their own clan, and with no territory of their own, they have to find a new "lord" to serve just to get a meal. But entering a lord's service is a two-way thing: just like you can't become a civil servant today just because you want to, you gotta pass some tests and the government's got to want you.
