There are specific differences in the dictionary meaning of words accountability and responsibility. In the ITIL world, we also use these terms and often in different contexts too…
When we write accountability, we are referring to a role which oversees a specific function, action or responsibility
When we write responsibility, we are referring to a role which is actually performing the function, action or activity within a process
e.g. the roles of Process Coordinators vs. Process Owners… Mostly Process Owners would be accountable for the process quality and adoption, however its the process coordinator who is actually ensuring process quality by continuously looking at the data, identifying training needs and establish error correction plans…
In one of the projects that I worked on to improve process definition and introduce process updates, a role of Outcome Manager was defined. I like that term! It simply mentions the responsibility of that role as soon as you read it! I hope to have such relevant roles attached to ITIL Process documentation too!
Words like these are commonly referred to in the RACI charts, which are also called SOD (Separation of Duty) Matrix by some organizations.
Read a few more thoughts on RACI in ITIL by ITSMwatch columnist David Mainville here and a good article on wiki here.