"I draw a picture."
Supposedly (source: jisho) the kanji for kaki we learned in the previous lesson is the same for writing as well as drawing and painting. So what's with the use of different kanji in your sentence? Also flabbergasted at Duolingo for suddenly only providing hiragana for kakimasu in this example.
From what I've learnt, one uses the kanji 書くwhen referring to writing, and hiragana かく when referring to drawing. Alternatively one can use 描く, read かくor えがくfor drawing.
I think it's slightly easier to understand this if you think of え as a drawing and not a picture
No, both are different kanjis with different meaning each although they are homophones.
描く is the kanji for drawing.
My bad kakimasu is to write I guess I learned the more precise verb 描きます
This doesn't pertain directly to the above sentence, but just so you see the difference between two similar kanji: 猫を描く(ねこをかく) means "I draw cats". Note the difference between the dog radical (犬/犭) in 猫 and the hand radical (手/扌) in 描く.