Yes, if you make a folder on the desktop, then drag everything on your desktop to that new folder, when you put it in the trash, not everything will go in the trash. There's a few special icons - usually for external storage, and for other partitions on your hard drive, that can be moved to a folder, but won't go in the trash. That's part of how the desktop works.
Question: Why do you need to put ALL items on your desktop into a new folder?
They are already in the special folder in your user folder, named Desktop.
Are you naming a new folder "Desktop" for some reason?
That is a reserved name, so be sure to name it something else. Even "All my desktop stuff" would be a better name.
You CAN go to your Finder Preferences (under the Finder menu), and make changes to what kind of devices will show on the desktop. That can help you avoid confusion when you try to get rid of clutter on the desktop in the future.