Those seem to be all I have?
That is because you are using an older version of Blender.
Kent uses 2.81 for this course, so you must have 2.80.
The sculpting part of Blender is under heavy development and the latest stable version is 2.83.4, which has even more brushes:
Makes sense, I could've checked that for myself haha . Anyway, thank you very much for the quick answer!