Indeed many info pages have the same content of the manual pages. It is just another format to display them by means of different applications or to print them out in a number of formats using texinfo utilities.
The info source files are located in directories specified by the INFOPATH environment variable, e.g.
$ echo $INFOPATH
Almost all GNU applications provide an info page, usually placed in /usr/share/info. In my opinion one of the most useful is
which provides many more information than the manual page. Look at it and see if its content is different from "man date".