Bind C-i and TAB keys to different commands in terminal applications via .inputrc

For what I have tried, TAB and C-i in .inputrc seems to mean the same thing, whatever I bind to one is bound to the other. I know that originally, it was the same thing and that this behavior is kind of inherited from the old times but nowadays, apart from terminal emulators, all X applications makes the difference between a C-i and a TAB press.