Please describe what an integrated bottom bracket is The article on bottom bracket terminology at Park Tool and the Wikipedia article do not say what an integrated bottom bracket is and other resources online assume the reader already knows what one is. What is it? How does it differ from a BB that is not integrated? What is "integrated" about it?
There is no such thing.

The only mention I can find is the Wikipedia article where it is used to describe the setup that is commonly known as two piece crankset. Wikipedia does not cite any sources for the term, so it is most likely that the editor simply invented a word to describe a setup similar to external bearings where the bearings might be inside bottom bracket shell.