Original version - The dollar looks like an ordinary dollar.
Patrick's version - In order to hide that the dollar got covered with paint, Patrick drew on it with crayon, which was ineffective, as it looked nothing like a real dollar, despite Patrick thinking Mr. Krabs would believe it.
Role in series
SpongeBob and Patrick get paint on Mr. Krabs' first dollar while painting the inside of his house. The two then try various methods to remove the paint, all of which backfire on them. Patrick later colors it to look like a dollar, which just ruins it further. However, Mr. Krabs is able to remove the paint with his saliva.