Block Painting
A block painting website gives you a tool to paint with, most likely a paintbrush-looking cursor, and a color palette. After you click on a color to load your paintbrush with color, you can then start clicking around on the image to fill in the color. With block painting, you don't drag your mouse as if you're drawing. Instead you click, and it automatically fills in a predetermined area with the color. This is a really good type of game for younger kids, as it shows them how to stay within the lines and gives them quick results with just a few clicks of the mouse.
Freestyle Painting
A freestyle painting website will give you the same tools -- a color palette and a brush-like cursor to use. The difference with freestyle, though, is that you have complete control over where the color goes. If you want one leg to be two different colors, then go for it! This is more appropriate for an older child who wants to spend a little more time making his picture just right.
Safety
With either type of online painting game, it is important to exercise supervision. The age of the child will determine just how much supervision is needed. It is necessary, though, to make sure there are no errant clicks that either take them to inappropriate websites or take them delving into your computer's hard drive.
Saving and Printing
Because of the nature of these painting games, you aren't allowed the ability to save your work, but you can always print your work and save a hard copy. Even if your children don't suggest saving their work, make sure to print out at least a couple of their masterpieces so they can admire them on the fridge later.