Authority and responsibility can, in a sense, be contrasted with accountability and delegation.
Authority is the power to make decisions and to be "the boss." A person in authority is really not accountable to anyone. This is because accountability means having to account for your actions to someone. The person who holds the highest authority in a firm, for example, does not have to account for their actions to anyone.
Responsibility means that you are the person who must complete a task and get it done correctly. This can be contrasted with delegation because delegation is the process of giving part of what might be your job to someone else. That person then becomes responsible for getting it done correctly.
These are not perfect contrasts. A person who delegates will, for example, still be responsible for the work of his/her subordinate. But these are general ways in which these concepts can be contrasted.