The OEM license versions of Windows are intended to be bought by hardware vendors and system integrators so that they can install the OS on their systems before selling them on to customers; for this reason the price is slightly lower than the retail version.
Buying an OEM version to install on a system yourself is a bit of a gray area. It’s not what the license was originally intended for (to help SIs reduce the cost of their systems by taking advantage of bulk purchases). You shouldn’t really be able to obtain an OEM license that is not sold with a complete computer system, but many retailers completely ignore this, or keep within the wording of the law (but not the spirit) by selling it along with a nominal piece of hardware.
Because the OEM version is only supposed to be sold with a complete system the end-user license agreement (EULA) differs slightly with the retail license in that the OEM license is not transferable to another system, whereas if you purchase a retail version you a free to transfer the software to another system as often as you want. Even a pre-bought system can be upgrade though, so (as your friend says) the cut off point as far as Microsoft grants as to what constitutes a different system or just an upgrade is with the motherboard.
Whether you have a retail license or an OEM one, what you are hoping to do is against the terms of the EULA. You can’t install the OEM version on 2 systems (motherboards) and you can’t install the retail version on a second system without removing it from the first system.
In practical terms though most of this is just words. Whether you buy the retail or OEM license you will have to activate it, and if you install on 2 systems you will have to activate twice and need to give a good reason why. The important fact is that Microsoft cannot tell if you are activating again because you are illegally trying to install on another system, or because you have upgraded an item of hardware. As long as you give your reason as, “I have just upgraded my xxxx.” Where xxxx is a piece of hardware but NOT the motherboard you will be able to activate.
If you want to be fully legal, buy 2 retail licenses.
If you want to be legal and save some money, buy 2 OEM licenses.
If you want to be legal on one system and have a bit of flexibility in your lies for a little extra expense, get 1 retail license.
If you want to be cheap, get 1 OEM license.