This is a great question and one that is appropriate for today's world, as many people spend more and more time on the Internet. I would say that an online friendship differs in three very important ways.
First, online friendships are handicapped, because they are not able to get to know people in different modalities. There is no physical contact, little picking up of gestures, body language, and other elements that are present in a face-to-face relationship. For instance, you cannot travel together.
Second and more importantly, online friendship are usually based on convenience. You get to check messages when you want. You get to reply when you want. In fact, you can go online only when you want to. There is little social responsibility. Hence, online relationships have a hard time growing. Often times, friends become closer as they help each other out in hard time. In short, you are there for each other; online friendships rarely do this. And when online relationship do this, it is often because there is already a face-to-face relationship.
Third, online friendships are usually very broad. This means that you can have hundreds of online friends. For example, some people have over 1,000 Facebook friends. This does not mean that all these people are actually friends. Broadness and superficiality (which are not necessarily bad) replace in depth relationships.
One final point, online friendships are not always bad. The lack of formal contact can make people open up much better. This can be judged a positive point in some ways.