It's not clear to me what the question is. The Uno's microcontroller is the ATmega328P. The Nano's microcontroller is the ATmega328P. The most significant difference between the two is that the Nano has pins A6 and A7, which the Uno does not. This is because the original Uno used the DIP package of the ATmega328P, which doesn't have the extra two analog input channels. The Nano has always used the SMD package of the ATmega328P, which does have the extra two analog channels. The Uno is now also sold with the SMD ATmega328P package, but they still didn't break out A6 and A7 on the SMD Uno.
The Nano has traditionally used a different bootloader than the Uno, which takes a 2 kB boot section and uses 57600 baud communication speed for uploads. The Uno uses the the optiboot bootloader, which takes a 0.5 kB boot section and uses 115200 baud for uploads. The official Arduino Nanos were changed to start using Optiboot as well last year, but they left the boot section at 2 kB. I have not heard any reports of clone or derivative Nano manufacturers switching to Optiboot yet.
The Uno uses ATmega16U2 USB to TTL serial chip, while the Nano uses the FT232. For most people, the only reason they would care about this is that different drivers are required for each, but these drivers come with the Arduino IDE. Some people have taken advantage of the programmable nature of the ATmega16U2, but this is quite rare.
There are some other small differences in the hardware you could see from comparing the schematics.
However, none of that makes any difference for the project avalon66 wants to do.