Arduino Nano ATmega328P bootloader difference
The bootloader currently shipped on the official Arduino Nano boards and selected via the Arduino IDE's Tools > Processor > ATmega328P after choosing Tools > Board > Arduino Nano is the same version of optiboot used by the Arduino/Genuino Uno:
https://github.com/arduino/ArduinoCore-avr/blob/master/boards.txt#L152

nano.menu.cpu.atmega328.bootloader.file=optiboot/optiboot_atmega328.hex


https://github.com/arduino/ArduinoCore-avr/blob/master/boards.txt#L72

uno.bootloader.file=optiboot/optiboot_atmega328.hex


The bootloader selected via Tools > Processor > ATmega328P (Old Bootloader) is the "ATmegaBOOT" bootloader.

As used by the Nano hardware definition, there are two significant differences between the two bootloaders:


Optiboot will not go into an endless reset loop after a watchdog reset. ATmegaBOOT will.
Optiboot expects the upload communication at 115200 baud. ATmegaBOOT, 57600. This is the reason why the old boards don't work with the Tools > Processor > ATmega328P selection and vice versa.


There is another very significant difference between the two bootloaders that, sadly, you will not benefit from with the new Arduino Nano board/hardware definition: Optiboot will fit in a 0.5 kB boot section, while ATmegaBOOT requires a 2 kB boot section. Unfortunately Arduino forgot to change the BOOTSZ fuse accordingly and so the opportunity to free up 1.5 kB of precious flash memory for the users of the Nano was lost. The willingness of Arduino to knowingly release flawed hardware has historic precedent.


  I haven't been able to find any release notes about the bootloader.


Arduino's release notes have not yet adapted to the fact that hardware packages may be released independently of IDE releases ever since Arduino IDE 1.6.2. There is a note about the bootloader change in the IDE release notes for the next IDE release:

https://github.com/arduino/Arduino/commit/ec179e5af67b7f1eeb5e46d22034798f8b24b7cb

Other than that, you can consult the commit history:

https://github.com/arduino/ArduinoCore-avr/commit/1b14cc07331268e95eddcce2cc67e29ed667e62f