Can I install OSX to a Macbook Pro downloaded from a Macbook Air?

Okay, so a friend with a Macbook Pro wants to restore her Mac due to a password issue.. The problem is she has a bad internet connection and can't download OS X from Recovery Mode. I have a spare USB lying around and made an OS X Bootable with OS X Yosemite downloaded from my Macbook Air.

Isn't OS X a bit different for every mac? Can I use the OS X I've downloaded from my Air and install it to her Pro?

Any answers will be greatly appreciated. Thanks.