Q: Are all iPhones manufactured the same?

Yes, there may be differences in models intended for original retail sale in different countries or regions - see http://www.apple.com/iphone/LTE/ for example and notice the model numbers for different areas.

A few years ago there wasn't there some controversy because FaceTime was disabled in iPhones sold in certain Middle-Eastern countries?

Facetime remains banned in certain countries - Wireless carrier support and features for iPhone in the Middle East - Apple Support  iPhones sold by Apple Authorized resellers in those countries will have FaceTime permanently disabled.  And used phones purchased anywhere, but which were originally sold at retail from an authorized reseller in those counties will also always lack FaceTime.