I am very new to Networking. When I was learning on, and configuring, a router as DHCP for practice...I stumbled over which ip address should I choose amongst many ! So, could someone clarify this confusion of differenciating addresses in general, (be it ip or else) ?

Too vague a question. But let's try this. Forget the IP for a moment and if you want to know the unique PC or device, look up it's MAC address which for most setups is static.

Now if some newbie IT staff thinks this is a solid solution to tracking a PC or device I turn on MAC randomization and see them lose the rest of their hair.

-> Again, what are you trying to measure or find out?

DHCP operates a pool of IPs for clients that need them. Usage is a bit worthless unless they stay assigned a long time. As noted, the mac from the ethernet layer is a better id.