Photos search count differs from displayed photos

Sometimes it just takes time for iOS to complete the scanning necessary to identify stuff, especially after an update. The scanning is done in the backboard so you don't really notice. And since scanning uses the battery, and since lots of people are very anxious about battery drain, the iPhone will avoid scanning when not plugged in. And since scanning uses processing power, and people hate slow-downs, the iPhone will avoid scanning while you use it. And since the background scanning requires the internet and bandwidth, the iPhone will avoid scanning when the internet connection is weak.

So, if you want the scanning to complete sooner, then find good wifi, plug the phone in, keep it locked, and leave it alone! All this applies to a lesser extent for the Mac.

I'm not sure what you're seeing. And, of course, we can't possibly know what's going on with your phone. However, when I search for "snow," I get this:

which shows different ways it has detected "snow," like as text or as part of a word or just apparent snow on the ground, with a few examples. If I select tap the top choice, or if I again hit the query button, I get 246 hits for snow-- and I live in Texas! (Until the last few years, we used to get snow from time to time, and Amarillo is still pretty harsh, but--oh, I've gotten off the subject...) As I look through those, they pretty much all seem to have snow in them.

On the other hand, if I select "Snowbelt" I get a Far Side Cartoon about dogs, and I don't know why.

Exactly how is your result different?