Responsibility is about meeting job expectations and fulfilling daily work duties. It must have a consequence or a penalty in case of failure.
Accountability is taking ownership of your role and doing what is right for the business. In other words, it is about self-responsibility, for it requires workers to accept the consequences for their actions or omissions. When people take ownership of their role and do what is right for the business, they're accountable. Accountability creates trust and pushes people to try innovative solutions to get their job done.
Have a look at the video below for a more detailed explanation and examples.