For the sake of sanity the following definitions will be loosely used:
When a near or exact clone is made of a classic game by a development team other than the original and does NOT involve the original publisher or license. These games often have names VERY similar or THE SAME as the game they are remaking. They are also very often released as freeware.
A LICENSED remake of a classic game that re-visits the same content while updating it for modern audiences. Sometimes by the same developer as the original but often not. Often created to start a new series.
Unlicensed sequel or remake of a game that features a similar name and theme, often has the many of the features of the original but does not have the official license.