One of the most useful and yet ignored principles in thinking about grammar is the consistent separation of categories and functions. When you can keep them distinct, analysis become much clearer. One grammar that is scrupulous in making the distinction is the Cambridge Grammar of the English Language. It clearly sets out the various categories on pp. 22 & 23, which I've visualized in the first image below.
Unfortunately, there's no clear overview of all the functions. I've tried to bring them together in the following graphic. As usual, if you see anything wrong or missing, please let me know.