Digital Art is a whole other ballgame to Tradtional Art, while using a similar process for creation (at least in the case of bitmaps) - Digital art tends to be a lot crisper and cleaner looking than traditional
Art programs generally come in 2 kinds of flavours, Bitmap and Vector. Some programs speciallise in one or the other, while one or two use both in tandem.
This kind of digital art is close to traditional in terms of input, the user draws by freehand and colouring can be done in a similar manner, though, being digital, this comes with a few benefits. For example lineart can be easilly filled by the "fill" tool (assuming lines are closed) and some programs can make instant gradients and special brushes that add certain effects. However due to user input, lines can be wobbly or imperfect and due to Bitmap being based on pixels, art often suffers artifacting from resizing and low resolutions, resulting in blocky images.
Adobe Photoshop is one of the most popular bitmap art applications out there, other programs worth considering for bitmap are programs such as the GIMP and Paint.Net.
This art style is based on co-ordinates instead of pixels, therefore the line is controled by the computer, though the user can manipulate the lines through handles and manual adjustment. Vector programs can be a little tricky due the lack of control the user has compared with bitmap, though vectors generally result in much crisper images and better line control (depending on the artist). Fiddling with vectors can also lead to some fun results as well.
Adobe Illustrator is one of the most popular vector packages on the market, though Flash has a form of vector art that takes a bitmap input style approach (user can draw like tradtional, though computer still has some control over the line, so it can auto-smooth and "guess" where the user wants the line to go, sometimes the input isn't quite exact)
There are few programs that manage to do both styles very well. Photoshop has vector tools but they are very limited compaired with Illustrator and Flash in terms of vector based-features.
Artrage has some vector capabilities in it's tools, with pen and pencil tools featuring smoothing, and a number of other vector based tricks to the other tools, though Artrage dresses it all up like a tradtional easel.