Unit and integration testing in web development is different?

I am pretty confuse with unit and integration testing of traditional software development and web development. I have seen many different answer and explanation of it.

The Web Engineering textbook says about unit and integration testing for web application:
Unit testing: Testing on single web page as opposed to testing single function
Integration testing: Testing on flow of data from one web page to another (and linkage)

while the software engineering textbook defines unit testing and integration testing as followed.
unit testing: Testing on smallest unit
integration testing: Testing on interaction between unit or module

Hope someone can clarify to me which is the correct one.