The differences between them are so subtle and minor that it wouldn't make much difference in spoken conversation. "...out on a date" defines "date" as a time spent with another person you like. "...out for a date" defines "date" as the person you like. "I'm going to ask her out on a date" is the more common way to express the feeling of dating someone. "I'm going to ask her out for a date" is less common, and almost implies that you expect the person to hook you up with a friend. Context would be the deciding factor.

Good answer from Jkduzz. Your question can be asked, "Do they have the same meaning? Are they interchangeable?"