Yes, Apple ID password ***** ***** same as iTunes password. It is the password ***** use to download apps, musics, books etc from iTunes Store or App Store.
You can reset the Apple ID password ***** here if you don't remember it --> https://iforgot.apple.com/
Remember, if you need to download anything to your iPhone you need to free space on your iPhone. You actually need to free the space of the physical memory of your iPhone. The space/storage you purchased is for iCloud
, i.e the space to store your iPhone's backup, documents etc online but not on your iPhone.
You can delete unwanted photos, movies taken on your iPhone, apps that you are not using etc to free some space. Make sure you delete the deleted photos and videos from "Recently Deleted" albums too in Photos app to free some space.
If you have any difficulty on following the steps above, please let me know and I will help you with that.