Does 2012 Prius Two have a differential?

There's no separate differential, no distinct gear oil replacement. Maybe download the pdf of the Toyota publication "Warranty and Maintenance Booklet". One source, under the "Manuals" tab. All the fluid changes Toyota wants are noted in there, albeit in hard-to-read, event-by-event format. Attached is a spreadsheet summary I've put together, both as-is, and extrapolated to 240k miles (Toyota stops at 120k).

What's the miles on it now, btw? I'd also consider these, mostly not in the Toyota schedule services:

EGR cleaning
Transaxle fluid change
Brake fluid change
Brake inspect/clean/lube (sort of in the schedule, very understated though, every 30k miles, but oft ignored)

 

Pretty much all front-engine, front-wheel-drive cars combine the transmission and differential into a single contraption, and call it a 'transaxle'.

The places you drain and fill the transaxle oil cover the whole works.

 

With 142k I wouldn't bother "diagnosing" the EGR, it'll be pretty clogged. Note too: there are crucial EGR passages in the intake manifold. I'd also start researching head gasket replacement (protracted neglect of EGR cleaning and head gasket failure seem to go hand-in-hand), and keeping an eye on the engine coolant reservoir level. The head gasket failure mode is typically coolant leaking into combustion chambers. Typically starts with cylinder one.

More info on EGR cleaning and head gasket in my signature. (if you're on a phone, turn it landscape to see signatures.)

Also would be very timely to change the engine water pump and thermostat. The generic name for the engine water pump is Aisin WPT-190. And from my notes:

Engine water pump:
Toyota p/n: 161A0-29015
gasket p/n: 16291-37020
Inverter water pump:
Toyota p/n: G9040-47090

This thread, pinned at top of this forum, has very helpful/informative videos (by @NutzAboutBolts), on most everything gen 3:

Nutz About Bolts Prius Maintenance Videos | PriusChat

Coolant changes (both inverter and engine) are included. The one exception I'd take with the engine coolant change: Toyota advises to let the new coolant level settle, keep topping up, and when it's stabile, fill to the "B" line, and install the cap. Then proceed with protracted running in maintenance mode. I did this, and the inverter coolant, a few days back, both for the second time. One clue I found to sufficient warm up: I thought it was done, crawled back under to start replacing the under panel, felt the two large hoses running to radiator under there, and they were still stone cold. I put it back into maintenance mode (allows car to run engine continuously), and just lay under there, checking those hoses, till they both got toasty.

The coolant changes instruction from repair manual attached, plus a few others. Anything you think of, just ask. .

 

Just search "Toyota factory parts online"

The dealers that sell online usually have a good part number search function that can go by VIN

Toyota Parts Now | OEM Toyota Parts Online Store

Genuine OEM Toyota Parts and Accessories Online - Toyota Parts Deal