Also, there are two containers for brushes in Illustrator on the iPad currently:
1) There is an in-built library of brushes (of Art and Calligraphic brushes) which you can explore and add to the document.
2) The brushes used in a document always stay within that document. This means if you open a document with brushes from the Illustrator desktop version on iPad or vice-versa, that document will bring the brushes along.
I hope it clarifies!
Please feel free to reach out if you run into any other questions or issues in the future. We'd be happy to help.