iphotomacmacosphotosstorage
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: 
There is no way to import an Aperture/iPhoto library except start a new Photos library and have it convert from an existing Aperture/iPhoto library.
I think the best solution would be to start a new Photos library based on your existing Aperture library. Attach your iPhone to the Mac and wait for it to appear in the sidebar in Photos, then import everything it will let you from the phone. Finally, set it as the system library (Photos menu > Preferences > General tab > "Use as System Photo Library") and enable iCloud Photo Library (Photos menu > Preferences > iCloud > iCloud Photo Library).
In theory this should cause the images from your new combined Photos library (old Aperture library + what was on the phone) to upload to iCloud, while also downloading anything in iCloud that does not exist in your new Photos library. And in turn, your phone should download anything new that is uploaded to iCloud.
The step of syncing from your phone directly to the Mac should not be necessary, but is a backup just in case iCloud freaks out with the change in the System Photo Library and removes what you uploaded from your phone. It also saves Photos from having to download any of those photos, assuming it finds them to be duplicates of what's in iCloud.
So after some time (learning python on how to monitor and plot library size and disk usage) this is what I have observed regarding my first question. As written by @will-mallard and @bmike the optimizer targes for percentage free disk space. As shown below: the size of the picture library increases and decreases together with my disk usage. During those three days I did not use my mac book air for work. I only added pictures two times.
Over a longer time scale, one can see the reduction of picture library disc space over time while I was working on my macbook.
My followup question is now: What triggers the optimization? At first I thought it is some kind of free space threshold. But as it is easily seen in the last plot, something at the 24th May triggered a reduction of library space. I am not sure what that was.
Best Answer
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 "Show Package Contents" 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 Libraryand~/Movies/iMovie Theater).Why the Size Changes
In a comment, you had mentioned that
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 "Add to Album," "Display Reference Photo," or "Instant Slideshow Controller." Furthermore, at.../Photos.app/Contents/Pluginsthere is, on my mac, two plugins. It's possible for this list to be modified by adding in other.appexfiles.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.