The true termite queen is the one that flew in, chucked off her wings and began the colony. She ends up quite large when, every time she moults, she gets another set of ovaries. The head and chest stay the same but the abdomen stretches. If she dies, some types of termites can replace her with one (usually a few) of the ones that are just beginning to grow wings. They are never quite as impressive and apparently, often only give birth to males. In some species, a replacement queen isn't possible and the colony dies.
In young colonies developing in the same lump of wood, it is common for early contacts to result in little battles and often as not the colonies merge. Despite our use of 'king' and 'queen', in the real world, colonies often contain several of each. These are generalisations, there are around 4,000 different types of termites and they organise themselves in a host of different ways.