That's a very interesting question! Normally, in American English, a meeting is a pre-planned time and place for getting together with other people. This is usually in order to talk about a certain subject, which is usually understood in advance. For example, "our company will have a meeting tomorrow after lunch to discuss how many new truck drivers we need to hire."
A meet, on the other hand, is usually a set time and place for a sporting event. For example, "those two teams are rivals. In fact, they hate each other. There will be a meet next Saturday at the fairgrounds. Be sure to see it!"
Hope this helps!