These two terms are basically synonymous. However, liability usually refers to a legal responsibility, while accountability refers to a social responsibility.
Here are some examples:
If I hit someone's car with mine, I am liable to pay the damages. On the other hand, if I get caught cheating on my girlfriend, I am not legally liable for any emotional damages, but I am held accountable socially by her and likely others in our shared social group.
I hope that helps!