The error lies in thinking they're 'real' systems to be taken for granted and blindly reasoned forward from, instead of sometimes-helpful academic categorizations.

You can always factor things into groups. e.g. 'Thoughts about now vs thoughts about the future'. Extending that to say there are therefore two modes of thinking and that the brain must handle your two groups differently, at some fundamental or physiological level, and there are only these two modes and all things are either one or the other ... is perhaps quite misguided without more support.

"It's only a model"