I'll bite.
Character for my part. Setting aside the knee-jerk queasiness I feel in the face of people using the word 'toon', it's a simple case of what the two words suggest. 'Toon' suggests a caricature, something simple and shallow usually created to a specific end - say, humour, or to portray something in an extreme light.
Character on the other hand suggests the sort of depth and complexity I want my, well, characters, to have. I like to imagine what they're like and create stories around them. Forra is a young spearman wandering around after he lost his adoptive aunt, Rorina is trying to smuggle herself and her sister away from an unpleasant stepfather, and T'aemi I like to think of as an opportunity to explore the idea of the 'generic adventurer'.
So when people call my characters 'toons' it.. feels like they're devaluing all I've imagined about them. I make it a rule not to stop other people referring to their characters as such, however much I might dislike it, because that's their choice. But.. it's true I don't like the idea of the word being put beside my creations, no.