I'm not sure if it's proper for me to answer, but:
The Biography is as named: Your character's background information.
Your Character Development Thread is the post that you are most likely to change more often.
You can use them to record future plot developments for your character, and also record future characteristics such as a Patronus (Even if you character is not of age to be able to perform that spell, sometimes this adds a bit of insight into your character's personality).
Also, people are open (and encouraged) to ask questions about someone in these threads to help your character develop. This wouldn't be very helpful in the Background Center, as questions about your character's history would seem more like criticism. After all, you may not be interested in changing your character's history, but you are probably more open to interesting new developments in your plots or personality.
It's a bit long, but hopefully this has made it clearer.
Glad to help