Good question!
That’s why we need research. We don’t know if they have a common cause or just a common mechanism of action. They very well could be the same disease; Lyme Disease is not well understood and has been implicated in all sorts of neurological diseases such as Multiple Sclerosis and Alzheimer’s.
But the link isn’t quite obvious enough and the potential treatments, which rules out government money; and aren’t considered to be profitable, which rules out commercial money. Good for Gates stepping in here