The main difference between responsibility and accountability is that responsibility can be shared while accountability cannot. Being accountable means being not only responsible for something but also ultimately 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 the 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 beinging in more supplies before they run out. At this point, you cannot say it is Tom's accountability. Tom is responsible for the office supplies, but he is only accountable and owes an explanation 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 as a result of the audits, ethics analyses and lawsuit that followed, one of which was founder and CEO Kenneth Lay. 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, Lay was found guilty on all six counts of conspiracy and fraud by the jury, making him responsible as well as accountable for the downfall of the company.