He found a page = He found an object He found that = He realized something

He found a page that had been ripped off his book = Suggests a page had previously been stuck to the front of his book, someone had pulled it off, and then he found the page after this had happened. 'A page' could suggest that there were originally several pages stuck to the book, one of which was pulled off. He found a page had been ripped off his book = Suggests a page had previously been stuck to the front of his book and someone had pulled it off. He discovered later that a page had been pulled off but unlike the previous sentence it is not clear whether or not the page is still there. If the page had been inside the book, the sentence should read, "He found a page that had been ripped out of his book". It would also be possible to say "Someone had ripped off a page in his book" meaning that someone had tried to pass off the contents of this page as their own work somewhere.

He found a page that had been ripped off his book. = He found the page. He found that a page had been ripped off his book. = He discovered the book has a page ripped from it. Whether he has the book and/or page is unknown.