Formal writing is like the stiff looking man who wears a suit all the time, who looks nice, but doesn't have much personality. He sits there wearing sunglasses (maybe he's a bodyguard) and doesn't move much but you get a basic idea of who he is just by looking at his regal stance. The writing in formal situations is restricted and voices are much more similar. It's harder to be unique and it is very structured most of the time. Of course, this doesn't mean that formal writing is always bad; there are lots of times when it can shine and stand out. It is a great way to persuade or get a point across effectively. If something is written very formally and intelligently then more people are bound to understand and agree with it. If it sounds more informal and opinionated then less people will resonate.
Blogging is so much different than what I just explained. For instance this blog post is not very formal at all and I am writing this using completely different technique. Blogging is like the weird hippie on the side of the street. They are full of expression and color. Their personality overflows just from their presence, and you can't miss their quirks and interests.