If you are signed in with your Apple ID, there is a connection to iCloud (whether you use it or not). If you are not signed in with your Apple ID, then you will not see the iCloud Download column (or an option to show it). In case you are signed in with your Apple ID, here's more info as an FYI...
iCloud Download is not a special "view." It's just one of the columns you can show (or hide) in Songs view. Make sure you are using the Songs view, which gives you the plain song list with columns. Click the control at the right end of horizontal bar to select the view, so that it says "Songs" (as shown in first screenshot below of the upper right corner of my iTunes window).
The second screenshot above shows the upper left corner of my iTunes window, after right-clicking the heading row of song list. In screenshot, the iCloud download column is already visible (with cloud symbol in heading); it has a checkmark in the show/hide columns menu. Note the songs with cloud symbol (in iCloud Download) column; that's an example of songs being accessed from iCloud (not local storage).
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For your actual problem, I think all of your songs are currently stored locally, because you can sync those same songs to an older iPod.
In original post, you said the iPhone showed 95 songs out of 115. In your latest post, the number was 90 out of 110. Assuming this is the same playlist and you updated it to remove a net total of 5 songs, it's somewhat odd that the number that remains "not accessible" on the iPhone remains 20. Do those 20 songs have anything in common? For example, are they the most recent additions to your library. Are they all iTunes Store purchases? Are they all songs you added from an external source?
Is it possible that those 20 songs were purchased from the iTunes Store using a different Apple ID? These would be older songs purchased before early 2009, when songs purchased from iTunes Store used DRM (copy protection). After early 2009, DRM was no longer used with song purchases. You computer can be authorized with more than one Apple ID, so they play (and sync) in iTunes. And on the older iPod, Apple ID does not matter (on the iPod), so as long as the songs sync, they play on the iPod. But on an iPhone, you are signed in with ONE Apple ID. So maybe you have songs (that use DRM) on the iPhone, purchased using a different Apple ID.
You can check by doing a Get Info on one of those 20 songs in your iTunes library. On the Info window, go to the File tab. For kind, a song that has DRM is Protected AAC audio file. You may also see a purchased by field showing the Apple ID used for the purchase.
If that's not the cause, I can't think of anything else, except for data corruption on the iPhone. What iTunes shows as loaded and what the iPhone shows as loaded are not "in sync." You may want to do a Restore on the iPhone using iTunes. BUT FIRST, uncheck Sync Music again, so that your iPhone does not have any songs loaded. THEN, back up your iPhone using iTunes. After the backup, do a Restore using iTunes (which erases the iPhone)
Use iTunes on your Mac or PC to restore your iPhone, iPad, or iPod to factory settings - Apple Support
After the Restore completes, restore your iPhone's data from the latest backup. Finally, set up Sync Music again using your 110-song playlist.