removing items in collections

I'm having a hard time removing items from collections.
I can 'move' the item to a different collection by right clicking and 'add to collection'. However I then no longer want the item to appear in the original collection that it was in. But if I right click and 'remove from collection' it deletes the item from everywhere!
How do I stop an item showing in its old collection, once I've added it to another?
Sometimes I can just drag it to the new collection and that works fine, and does remove it from the original collection, but sometimes it does not allow me to drag and I don't know why.
Any suggestions?
Thanks in advance!
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