Tightly coupled and closely held are ways to describe tight fitting pieces. If something is "tightly coupled" it means that it is thoroughly and tightly attached. For example: "The exhaust pipe on my car is tightly coupled to the engine." Closely held, in this case, also means snuggly fitting or attached closely to something. For example "The sign was closely held to the refrigerator by a magnet."
Usually when something is coupled it is completely attached and must be in place for the device to work. Couplings are used to attach one pipe to another to make it water tight, for example. When something is closely held it might not be a part of the actual machine, but it is attached tightly in some way.
Another example to explain the difference would be something like "The light switch is tightly coupled to the wall, but the painting is closely held by a nail."