The main difference between responsibility and accountability is that responsibility can be shared while accountability cannot. Being accountable not only means being responsible for something but also ultimately being answerable for your actions. Also, accountability is something you hold a person to only after a task is done or not done. Responsibility can be before and/or after a task.
It is Tom's responsibility to make sure there are supplies in the office room. So Tom will be aware of this task and keep bringing in more supplies before they run out. At this point, you cannot say Tom has been held accountable (answerable) for performing this task. Tom is responsible for the office supplies, but he is only held accountable — owes an explanation for his actions — if the supplies ever run out.
To cite another example, take the case of the notorious 2001 Enron scandal that led to the bankruptcy of the Enron Corporation. Members of the executive board were indicted for their illegal and unethical actions. CEO Kenneth Lay was one of the people indicted. Lay insisted that Enron's collapse was due to a conspiracy waged by short sellers, rogue executives, and the news media — implying that while he could be held accountable as the CEO and leader of the organization, he was not in any way responsible for the fraud in the company. However, a jury found Lay guilty on six counts of conspiracy and fraud, making the CEO responsible as well as accountable for the downfall of the company.