No, there is not really any difference between a citation and a ticket. A citation by definition is an official summons, especially one calling for appearance in court. A ticket has a definition of a legal summons, especially for a violation. The two words are interchangeable when discussing being written up by law enforcement for a moving violation.
A citation or ticket will only affect your insurance if you are convicted of the moving violation for which it was written up for. For example if it is for speeding and you decide to plead guilty and pay the fine then the court will inform your DMV so that the offense can be placed on your driving record. Your insurance company will then be able to see that offense the next time they pull your motor vehicle record (MVR).
It will depend up on your insurance company's rating system whether a certain offense will affect your rates. For example one single speeding ticket may not affect your rates, but likely will take away any good driver discount. However if you have already had a previous moving violation conviction on your MVR then this speeding ticket may cause your rates to rise.
Most states allow each individual insurance company to determine their own rating system and thus decide which moving violations as well as how many violations or accidents may affect your rates. The insurance companies then must file their rates with the state insurance regulator for their approval.