I did 'unlink' and 'remove' respectively, but really don't know how the two are different. What's the difference between them?
If your object is linked to more than one collection Object > Collection > Remove From Collection will give you the option to remove it from all collections or from one specific collection. Unlink in the outliner on the other hand only removes the selected object link from the collection it is in. If the object is linked to other collections, these will remain.