"Shakespeare's nickname is 'The Bard'. The word 'bard' means poet. Shakespeare is called 'The Bard' because he is widely recognized as the greatest poet the world has ever known. In 1769 the actor David Garrick wrote 'For the bard of all bards was a Warwickshire Bard'. This may well be the quote that started the nickname".

"According to  the Oxford Concise Dictionary, a Bard was a poet who was awarded privileged status in ancient Celtic cultures and who was charged with the duty of celebrating the laws and heroic achievements of his people. In modern Welsh usage, a bard was a poet who has participated in the annual poetry festival known as the Eisteddfod. The nostalgic mythology of romanticism tended to imagine the bard as solitary visionaries and prophets.  Since the 18th century, the term has often been applied more loosely to any poet, and as a fanciful title for Shakespeare in particular".

Good question. In my experience, he isn't referred to as "a bard," but rather as "THE bard."

The difference? Well, a bard is a poet, especially a poet from an oral tradition, like Homer. The term became a title: a way of labeling a poet and indicating that he (almost always a male) was extremely important, even great. Shakespeare is know as THE bard (okay, I'll stop capitalizing it) because he is known to be the greatest poet/playwright England ever produced. It is a way of honoring him.