Jira is an issue tracker at it's heart, and "ticketing" system is a sub-set of that. All "tickets" are representable as issues, off-the shelf in Jira, but not all issues are "tickets".
As @John Funk and @Dirk Ronsmans say, Jira Service Management is likely to be the best option for your "tickets". It allows people to create Requests which are backed up by Issues as a "ticket". The Request is what your customers see, the issue behind each one is what your helpdesk agents work with (because the issue is being used in an issue tracker, the people who need to deal with the issue have more information than the people looking at the request).
But you don't strictly need JSM to do it. Plain Jira is already a ticketing system because it's an issue tracker, and all your tickets are issues.
("Ticket" is not really a good word to use here; in native English, it implies a sense of entitlement which you probably shouldn't be assuming. But that's my English teachers explaining words in a lot more detail than most people need)
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