Hi c_kyr!
"Does every computer come with a "customized" version of tiger?"
In a sense, yes.
System install discs are computer specific, and cannot be interchanged.
And besides that, the
MacBook is
Intel, and I would assume that the
iMac, is
PPC.
Which definitely, are not the same.
Additional info in these links.
Using OS X Install CDs/DVDs On Multiple Macs
What's A Computer Specific Mac OS X Release
Software Update, Upgrade: What's The Difference?
If you call
Apple Customer Service, you may be able to order replacement discs, for a fee.
Be prepared to furnish all pertinent info about the
MacBook.
Such as the serial number, and all specifications.
ali b