<p>What is the difference between Object-Oriented Modeling and Object-Oriented Programming? I overheard a conversation on my subway train this morning and it seems that these things are different. Aren't they?</p>

I'd say the modeling precludes the programing, where the modeling is the physical design, before the programming is implemented.
http://en.wikipedia.org/wiki/Object-Oriented_Modeling
http://en.wikipedia.org/wiki/Object_oriented_programming