OEM is a component intended for use by Original Equipment Manufacturer's. It usually is a bagged piece of hardware, no manual, no cables, no frills. Just the essentials.
"Boxed" usually refers to a component packaged for retail sales. It includes the manual, and any required bundled cables or software.
The differences in guarantee or warranty period are based on quality control inspection data. OEM often units have a larger inspection sample, and are thus cheaper.
I have done very well with OEM gear. Usually if an electronic component fails, it does so in its initial use . . . traumatic failures caused by external events excepted. I can think of certain devices where a longer warranty is desirable . . . specifically TFT displays.
The rest depends on cost effectiveness. If the replacement cost is tolerable, you can save money by being "self insured." If you have no tolerance for such pain, then you need to spend more up front. Hard drives are a good example of this type of component. On the other hand, in over 10 years of building systems for myself and others, I have never had a CPU or memory failure.