How these two differ? I tried to read documentation but still can’t figure out. Is there any chance to emulate both of these somehow to see what visitor sees in real?
Google play search - how it happens in real? I have high play explore and very low play search with the app. How can it be fixed?
Explore is a traffic from Featured, Top Charts, and Similar Apps sections of GPS while search is a traffic directly from the search listing (when you type some keywords and hit search for the app).
Low search traffic may mean that you should work on keywords in your game’s title, short description, long description (it is similar to SEO) because user’s don’t use keywords that are there right now (or you use super popular keywords and your app isn’t at the top of the search result listing)
In other words I need concentrate more on text rather then on graphic elements(icon, big screenshot-thumbnail, game screenshots)? The problem is that I’m a bit afraid that fixing explore I can destroy good search ratio 
I was having the same confusion, especially after seeing different traffic sources in my Google Play Console. Turning to https://rankyak.com really helped me figure out the differences with simple breakdowns of where installs come from, like search vs explore. They show how users are finding your app and how to improve your visibility for each source. Worked out better than digging through scattered info online.