ATMEGA328P-U vs ATMEGA328-PU On my Arduino UNO the chip part number is ATMEGA328P-U, i recently bought a ATMEGA328-PU to make a standalone Arduino. realized the part number differences after receiving the package... 

I noticed that some arduino UNOs have the chip with part number of ATMEGA328P-PU! I'm totally confused!

Those chip are the same? can i use the one that i bought for an standalone Arduino?

If no what are the differences?
The main difference is the bit before the -. That is, the 328 vs the 328P.  The "P" there denotes "Picopower" which allows the chip to run at very low power consumptions. 

Basically the P version is a more modern version of the non-P chip.  There are probably other internal differences too but you will have to check the datasheets thoroughly for those.

Everything after the - is to do with the packaging and environmental grading of the chip.  For example PU is a -40C to +85C grade DIP chip. ANR is a -40C to +105C grade TQFP chip, etc.

If you see 328P-U then that's probably a fake chip. There's no such thing as single U suffix.