They have a little in common, but by far delete is used in the area of computers, when you get rid of some piece of information from the disk, server, etc. Deleted information is removed completely. "They deleted the names from the database." "We cannot recover the deleted files." (Remove is not good in those situations.) Remove is much more general. It means "take away". Maybe the thing is gone completely. "They removed the man from his position." "I removed the old paint and found beautiful wood underneath." Or I remove something and it still exists, but not in the original place. "We removed the carpet from the living. It's now upstairs in the bedroom." Interesting word combination!