In Florida a DUI is a crime. In NY depending on which statute you were convicted it may not be. That's the difference. If you were convicted of the non criminal offense in NY it would be off of your record by now. Nevertheless, it is always safer to be truthful.
In New York, DWAI = Driving While Ability Impaired and it a traffic infraction, not a crime. However, it never seals and stays on your record (I disagree with the other attorney's answer on this point). DUI is a crime. I can't speak to Florida law.
I am a former federal and State prosecutor and now handle criminal defense and personal injury/civil rights cases. Feel free to check out my web site and contact me at (212) 385-8015 or via email at Eric@RothsteinLawNY.com. The above answer is for informational purposes only and not meant as legal advice.
The infraction will remain on your record; both driving and criminal. Although it is not a criminal conviction like a DUI, it is probably best to answer the question with an explanation that the conviction was for an infraction and NOT a criminal DUI. Given that this involves your livelihood, you should consult with a Florida attorney.