Applying for PHD programs in FLORIDA. I have a question about legal questions?
A traffic offense would typically be something that resulted in a ticket (e.g. speeding) that you pay or, perhaps, go to traffic court. A DUI is decidedly a criminal offense that you can be prosecuted for in real (non-traffic) court.

As an aside, when you have a security clearance you absolutely must report arrests, but usually they will also explicitly mention a dollar value for traffic tickets, above which you must also report.

Good luck to your friend. They will need to be able to clearly explain the situation and the resolution.