These two Libraries can be combined, but they don't need to be. Double click on each one to open it in Photos so that you can see what's going on. Which ever you open last will be the one that Photos opens next.
The Library that Safari and other apps can access is the System Library. You can see which is the System Library with the Library Chooser which you can open by closing Photos and Option-clicking the Photos app icon.

You can also see if you have other Libraries, and the path to each. If you need to change which one is the System Library, you can do that at Photos' Settings>General. You didn't say if you use iCloud Photos, but the System Library is the one that Synchronizes with iCloud. In fact, if you want to combine the Libraries, iCloud works great for that-- they'll combine as soon as you switch the System Library.
If you have extensive albums and folders organization then, without iCloud, combining the Libraries can only be done with the trusted 3rd party app PowerPhotos ($40,) which can preserve the albums and folders as well as avoiding loading duplicates. PowerPhotos can be very helpful if you find that you want to continue with multiple Libraries. Many of us keep separate Libraries for archives.
I'll bet that new Library has many of the same pictures as the old one!