I did some searching to try and learn the difference but didn't find anything so I'm adding my two cents to the knowledge pot here.

I was looking for a flight for work. My corporate travel office website (which only shows unrestricted fares) wasn't giving me ideal flight routings so I started poking around with the United search engine. I found a good routing for the travel I needed (one UA flight followed by two flights on EVA) and did an advanced search for an unrestricted ticket. That specific request came up as "Not available". I did the same search again but instead of specifying restrictions I specified Y fare class. That showed as available; all flights showed Y fare codes, and much cheaper than anything that was available on my corporate travel website. As an aside, United did show a "flexible fare" (which ended up tracking to B fare for all flights) that was just a hair cheaper than the all Y fare itinerary. I figured that something must be up so I called the premier desk, explained what I was seeing and asked if there was any difference between Unrestricted fares and Y fares.

Turns out that just because the partner airline was showing as Y fares on the United search doesn't mean that it's a fully refundable/changeable unrestricted Y ticket. Apparently only the United portion follow those fare rules and the EVA flights were restricted: flexible, but not fully refundable. And that thing I said about the "flexible" fare having all B fares and was slightly cheaper than having all Y fares, turns out it was the same exact EVA tickets, only the United flight had different fare and that's why the price difference was so small. In the end, the cancellation/change fee for the "Y" fare or the "Flexible" is only $50, but my company has restrictions on buying any fares that aren't 100% fully refundable tickets (as a matter of principle I guess). Hopefully someone can get something out of this and avoid some headache down the line.