The modern words we have for drawing tablets: draw, tablet, pen, stylus are also ancient.
Tablet comes to us from Latin tabula which had the senses of "a board", "plank", and very relevant for us "writing table". More here: https://etymonline.com/word/table
Stylus comes from Latin stilus where has the sense of a rod with a pointed end and intended for writing or making marks. More here: https://www.etymonline.com/word/stylus
Pen comes from Latin penna meaning "feather". As you may remember, a feather being hollow when dipped into ink can be used as a writing device.
Draw is related to drag and both come from Proto-Germanic *draganan. The sense of these words comes from pulling something along. In the "draw" sense it is a writing instrument. In the "drag" sense it is any load. Even today you can see the word draw used in ways that don't have to do with creating pictures but rather the "pulling" sense - "Sally draws water from a well", "the sheriff drew his gun", "I had a blood sample drawn". More here: https://www.etymonline.com/word/draw and https://www.etymonline.com/word/drag.
There is no right term to use. An equally good case can be made for either word. I prefer using "pen" over "stylus" only for these reasons:
It's a more common word
Many drawing tablets manufacturers brands use the word "pen". Example: Wacom Pro Pen 2 and Samsun S Pen.