Now I got it.
1. When you download an app from AppStore, that "purchase" (even if free of charge) remains tied to the Apple ID used to download it, so that you can delete it from your iPhone, but the app is still available when you want it back.
2. If you don't make a backup (via iTunes or via iCloud), when you set up a new iphone with the same Apple ID, you can't transfer your old data, apps, photos, settings, from old to new device, so that you must set up everything (and install again all apps you downloaded, and yes they have a cloud symbol on the right, but it's not your iCloud storage, it means that those apps are saved among your purchased apps)
3. I strongly recommend that every user make a backup of his/her iPhone content frequently, to avoid any risks.
4. Recover (or restore) info from a backup is a quick and easy operation. In addition to what I've already sent in my first reply, please read this:
Restore your iPhone, iPad, or iPod touch from a backup - Apple Support
My english is not good, I know, but I hope you understand.
Let me know if everything is clear now.