Actually, I think it's the same cap except one is beat to $&!^. In your photo, you can see the tool marks in the new one which have resolved in exactly the places as the old one, just not as deep.
Answer -- it was the cap. And now you have a complete valve if you ever want to replace any other parts except the float. For that price, I'm guessing they sold you the white-cap 528, but all you needed was the cap. If you got a 528MP, then you got a really good price.
I'm so happy we were able to get you back in business with a relatively-minimal hassle. Now that you're up and working, you can still consider reporting the failure to Toto and seeing if they'll send you a new valve; that way you can put it in the drawer until next time. Taking the whole valve out actually is pretty easy, you usually can unscrew the mounting nut on the old one by hand or with one application of pliers, and then you have everything new when you put in the new one. Toto customer service is at 1-888-295-8134. Note it's an 888 number not 800.
Wouldn't hurt to check your water pressure, and if you have a closed system, verify that the expansion tank has not failed. There are lots of threads discussing closed/open water supply systems and the use of an expansion tank. WHere I live, one is required, period, even in an open system. Now, it doesn't do much there, but if the water company ever upgrades the meter or supply, it could easily become a closed system and you're already prepped for it. The Korky valve shuts the water off fairly slowly, but if there's another device around nearby that is fast acting, water hammer could pound that seal pretty hard. Maybe a hammer arrester would help.
Important note - I'm not a pro
Retired Defense Industry Engineer
Thank YOU for starting what has turned out to be a fun and informative thread. Jim and Gary have posted quite a bit of good advice on water pressure around this forum, including how to use a $10-or-less meter to check it and what to look for with respect to expansion tanks. The diaphram in that cap was really squashed, so it occurred to me that maybe it was a water pressure issue, but that's not my expertise so it was good to see others weigh in on it.