Finding the differences in a series of power supplies

Some Asus ROG Strix PSUs market themselves as having GaN transistors, yes.

Of course, given that ATX power supply vendors produce a standard-sized product, and they're limited to the ~1600W that Americans can draw from their 110v sockets, the GaN products are neither smaller nor higher power (though they might run a bit cooler or more efficiently).

Not really a fixed relationship between the two. Sometimes the entire blueprint of the PSU is from a different OEM. Corsair did this back in the day for a while where their HX750/HX850W PSUs were all made from a CWT design, their 1000W PSU was made from a different CWT design, and their 650/620W PSUs were a Seasonic design. I think this is less popular these days, but I think that's about as extreme as the difference gets.

At the component level, the focus is often on the sourcing and tolerances of the capacitors, which are used to clean up transients (very important) and power flow correction, among other things. I think the next most important components are the AC/DC conversion and the voltage transformers. Specifically for higher wattage PSUs vs lower wattage PSUs, the major difference is the amperage along the 12V rail.

A rough chain is: Outlet -> transient clean up circuit -> AC-to-DC conversion -> power factor correction -> PWM circuit (pseudo DC-to-AC) -> 3.3V/5V/12V transformers -> AC-to-DC conversion -> power delivery circuit (separate for 12V/5V/3.3V) -> power to components. The biggest difference between the wattages (if you keep the design fixed) would likely be in the power delivery circuit