First UEFI is the type of firmware that is being used to access the hardware as the computer boots.
Bios is the older type firmware.
They both do the same thing, but have different built in abilities.
UEFI provide more features. Well it does, but Puppy really does not need them.
The biggest feature is secure boot enabled and ability to support it.
When computer boots.
You press the power button on your laptop/desktop.
The CPU starts up, but needs some instructions to work on (remember, the CPU always needs to do something).
Since the main memory is empty at this stage, CPU defers to load instructions from the firmware chip on the motherboard and begins executing instructions.
The firmware code does a Power On Self Test (POST), initializes the remaining hardware, detects the connected peripherals (mouse, keyboard, pendrive etc.) and checks if all connected devices are healthy.
You might remember it as a 'beep' that desktops used to make after POST is successful.
Finally, the firmware code cycles through all storage devices and looks for a boot-loader (usually located in first sector of a disk).
If the boot-loader is found, then the firmware hands over control of the computer to it.
This is good info on differences of bios and UEFI firmware
https://www.freecodecamp.org/news/uefi-vs-bios/
To fully support all the features of UEFI you need a boot loader that provides that.
Grub2 boot loader does
If you are using Grub4dos as the boot loader.
It works OK with UEFI as long as you have secure boot disabled and/or the UEFI set to legacy or CSM mode.
I have computers with UEFI setup in normal operation, booting with Grub2 and secure boot enabled.
Must also install Puppy security key on the computer.
As far as what you see happen, as the computer boots, and Puppy Linux reaches a working desktop.
Both setups look the same as they boot.