What is has to be different about a ceiling fan on a covered patio from that of one in the house?

It it is not exposed directly to the elements, it is recommended you use a UL Damp listed fan, but plenty of people install regular fans. If it is to be in contact with water then a UL Wet Listed fan is required.

I personally recommend using industrial/commercial ceiling fans. Cheaper and better air movement. See:

Outdoor ceiling fans - Ceiling Fans N More
Industrial and commercial ceiling fans - Ceiling Fans N More
Ceiling Fan Brand & Manufacturer Recommendation - Ceiling Fans N More
Industrial & Commercial Ceiling Fans - Ceiling Fans N More
Industrial and Commercial Ceiling Fan Brand Guides and Reviews - Ceiling Fans N More