To be honest, there is no real difference in meaning, when we are using the word to identify one precise or exact thing.
However, the word 'particular,' can also be used to describe a person... "A particular person," is a person that insists that everything is done in a certain, particular (or specific) way.
So you would use this by (for example) saying "He is a very particular person."
Note, you cannot use the word specific in the context of the sentence immediately above.