Here's your definitive answer

(don't know how I missed the original thread)-you can be considered a daimyo and still be in service to a more powerful daimyo in the Muromachi/Sengoku period (things changed in the Edo period). "Clans" is actually a very poor way to describe the Oda, Hojo, Takeda, etc-in academia they're usually referred to as 'houses' because most of the vassals aren't related by blood. So in the 'house of Oda' you have many daimyo-Shibata, Maeda, Hashiba, Akechi, Sassa, etc. Even houses like the Hojo had daimyo under them like the Chiba. Back in the late Heian/early Kamakura, this ends up confusing a lot of people. You may have seen the name 'Minamoto' equated with 'Genji' clan or the Taira equated with 'Heike/Heishi'. However, Minamoto/Taira are the clan names, and Genji/Heike represent the houses of which these clans were leaders. Because of this, you would see Taira families that were Genji or Minamoto families that were Heike. Just like in Sengoku, blood ties were no guarantee for being allied. So when you see 'Clan', think 'House of' instead.
So in game terms, Sengoku uses 'clan' as 'house'. The clan leaders are indeed daimyo, but the game needed a way to set them apart from the lower ranked daimyo and used 'clan' instead of something like 'uji' (the developers told me they wanted to use as little Japanese terminology as possible in order to keep things less confusing to the game's largely Western playerbase).