I don't know if this is a prescriptive rule or not. Maybe I am just ignorant about this. However, I often write "Over 1900 faculty members attended this conference...", and our editors always change it to "More than."

What is the difference?

Kalleh, a good first place to look is Merriam-Webster's Dictionary of English Usage. Here's (link) what they have to say about this "hoary American newspaper tradition" of using more than in place of over. The editors' opinion: "[t]here is no reason why you need to avoid this usage."

The one and only motivated grammar: over = more than