I'm not sure whether there was an update in the installation discs between 2007 and 2008, when I bought my computer.
Even if I knew a way to use another version's install media ... which I do not ... posting the info here would not be allowed since I'm sure it's a violation of something somewhere.
If you got this MacBook new in August of 2008 then guessing from the MacBooks listed on everymac.com for 2008, you apparently have an early 2008 MacBook. So, yes, it is possible that your MacBook requires updates included in a later version of Leopard than your friends 2007 MacBook required.
Another (remote) possibility is to call a local Apple store and see if they would help you out with the reinstall. I tend to doubt that they would, but it never hurts to ask, perhaps?
What I would suggest is that if you really need to install OS X to your MacBook then pop down to a retail store and fork over the $30 to $40 for a Snow Leopard "upgrade" retail disc and install that. FWIW, IMO upgrading to Snow Leopard is worth doing in any case. Especially when it costs so little to do it.
- Note: If what you want to use is one of the iLife applications not just OS X, then the Snow Leopard retail disc won't help you. The retail install disc only includes OS X and X Code support. The iLife application suite included on the install media which comes with a MacBook is separate retail product from the OS X retail install disc.
Do not be put off by the word "upgrade" in the description of the Snow Leopard retail disc. Apple's upgrade is not like a MS upgrade. While the license agreement for that install only allows you to upgrade from Leopard, the technical truth is that it is a complete install disc.
You can upgrade an existing installation or install to a bare hard drive. You can use it not only to upgrade from Leopard but also from Tiger. (Or at least that's what I've read).
One caveat. If you decide to get a Snow Leopard retail disc try to get the latest version you can. This is probably 10.6.3. While you don't need it to install, it will save you some time because you won't have as much to download to update the OS after the install.
It occurred to me after posting the stuff above that if you are willing to risk it, another approach you might try is to boot your MacBook in target disk mode, connect it to your friend's MacBook using a firewire cable, and use your friend's install media in his MacBook to install OS X onto your MacBook's hard drive.
If this works then you might also also need to also use your friend's MacBook to update the installation to the latest (or at least a later) version of Leopard. Again, I just don't know if his version of Leopard will run without problems on your MacBook.
I frankly have no idea if any of this would work or not. But if you are careful it shouldn't hurt anything (much ... apparently your OS X install is already toast?) to try. Your call.
Taking the above yet one step further and, as always, if you and your friend can agree on it, you could simply temporarily move your MacBook's hard drive into your friend's MacBook. (I'm pretty sure the 2007 MacBook also uses a SATA hard drive).
Then just use his install media in his 2007 MacBook to install Leopard to your drive. Then update the install to the latest (or at least a later) version of Leopard. Then move it back to your 2008 MacBook. It seems like this should work, no?
Or you could use an external drive enclosure for your hard drive together with your friend's MacBook. This should also work. I've installed Leopard to an external USB attached hard drive using my early 2008 MacBook. I would expect it to work with a 2007 MacBook as well.
But Target Disk Mode would seem to be easiest way to go, if it works, since you don't have to track down the proper screw drivers and remove/replace any hard drives. I've never tried installing to a Mac in Target Disk Mode though so I can't offer more than the suggestion.