No, the other kind of draw
I was looking over some things at work today, and realised that the word 画 (huà) had been used as the translation for both draw and paint. I brought it up with the author of the document, and she said that there was no difference in Chinese, and asked if there was a difference in English. I told her it was quite a big difference (draw being associated with pens, pencils, crayons, etc., and paint being done with, well, paint). She discussed this with another colleague for a while, and I looked up 画 in the dictionary.
It happens quite often in Chinese that one character means several different things, with the meaning usually worked out from the context or the other characters around it. In this case, the meaning, to Chinese people, is the same. It makes a lot of sense when you think about it, as traditional Chinese calligraphy was done with a brush, not a pen.
In the end, as I did want to distinguish the difference between the two English words, we compromised with 画 (油画), where the first character (yóu) is the noun paint, and 画 means…paint. And draw.