Typical CUT and PASTE
For many user interfaces, whether graphical or not, there exists a method to move an object or collection of objects from one place to another. Sometimes there will be a button or command to MOVE but, because the user must specify what is to be moved and where it is to go, it is by its nature a two step process requiring the user to specify both a SOURCE and a DESTINATION.
If source and the destination are in different contexts, for example in separate windows not both visible, the user may have no way to specify both the source and the destination in the same command. One may not be able to move the pointing device (the mouse) in such a way as to indicate both the source and the destination without performing some action to change the contexts in between. Thus is born the CUT and PASTE commands. It is like a MOVE but in two steps. The source and destination are specified in separate commands and may have other activities (changing the context for example) performed in between. So CUT marks the object (sometimes visualized by saying it is "placed on the clipboard") and a subsequent PASTE command copies them to the new location while deleting the original.
That last part is very important here. If you don’t delete the original then the action is identical to a COPY and PASTE. That is, of course, a two step version of the copy command.