Why the Limit of Songs Across Devices in Apple Music?

I have three devices that share my Apple Music library: my iMac, my iPad Air, and my iPhone. The iMac shows the complete library, including all the playlists. But both the iPad Air and iPhone don't list all the playlists, in fact the iPad Air shows most of the playlists but not all while the iPhone shows only two of my playlists.

I do have many playlists. But a while back, someone wrote on the Community that Apple will show only 100K of the songs listed in anyone's library. Is this true?