Why Photos and Photo Library differ in size? Today I saw that 2 different positions in "manage storage" menu differ in size: Photos and Photo Library. I would like to know what is stored in which, but it is my first Mac and I cannot (or do not know how) simply check what lies underneath - both positions opens in the same window of Photos app.

Screenshot below:
I checked the file sizes on my computer as well:

As you can see, my Photos application is 56.4 MB, while my Photos Library is 13.38 GB.
What's Going On
The reason that the Photos application is so small compared to the library is because the application only contains the files necessary to run the application - you can right-click and select &quot;Show Package Contents&quot; to confirm this. The library, though, is stored externally, by default in ~/Pictures/Photos Library/, and all of your photos are stored there instead of in the app.
I believe the reason the application works this way is so that you can store your files externally, saving space, while keeping the core application internally, where it doesn't take up much space but still runs more quickly than accessing an external drive. Note that you can move your Photos Library and/or use option+click on opening to select a different library to flip through.
Other native applications that work in the same or a similar way include iTunes (files stored in ~/Music/iTunes), Photo Booth (~/Photos/Photo Booth Library), iPhoto (RIP; ~/Photos/iPhoto Library), and iMovie (~/Movies/iMovie Library and ~/Movies/iMovie Theater).
Why the Size Changes
In a comment, you had mentioned that

It was one of my suspicions, but initially I am sure I saw, that it was bigger than 294mb (approx. 1GB), so it looks like it also changes in time.

This is entirely possible. You don't say how long ago you saw it being that large, but Photos does contain some files that can be accessed by other applications as well, such as those contained in .../Photos.app/Contents/Library/Automator, which, on my copy, contains 13 Automator actions which can be inserted into workflows, such as &quot;Add to Album,&quot; &quot;Display Reference Photo,&quot; or &quot;Instant Slideshow Controller.&quot; Furthermore, at .../Photos.app/Contents/Plugins there is, on my mac, two plugins. It's possible for this list to be modified by adding in other .appex files.
The simplest explanation for what you're seeing, though, is that the software was updated in a MacOS software update at some point. Remember that the filing system was completely overhauled in High Sierra; perhaps a corollary to different files being stored differently is that they are now smaller.