A useful distinction
A grid provides positions; tiles can describe what belongs at those positions. A map may use those tiles for appearance, movement restrictions or both. A dark square is not automatically an obstacle unless the rules give it that role.
Put it into practice
Make a small paper map with a legend stating each tile’s meaning. Trace one permitted route and one blocked route. Keep visual symbols distinguishable and document whether the boundary itself can be crossed, rather than relying on unstated assumptions from another game.