A closure plate and a register plate are not the same.
A register plate is used when a chimney has no stainless steel liner. It closes off the chimney at its base, just above a wood burning stove. It acts as a barrier to prevent the smoke and fumes in the chimney entering the room. The register plate must therefore make a sturdy seal between the room and the chimney and MUST be made of galvanised or stainless steel (or other non-rusting metal) at least 2mm thick.
Why does it need to be made of metal? Well if a register plate failed then smoke could enter the room. This could happen, for example, if a brick fell from inside of the chimney.
A register plate will usually have access doors to allow the sweep to access any chamber above it to remove fallen soot.
It is rare nowadays that chimney liners are not fitted (although stove flue pipes might be connected directly to pot lined chimneys) and therefore register plates are less common on new installs. Modern wood burners are highly efficient and this means that LESS heat goes up the chimney. It is the heat that gives the draft (hot air rises and the hotter then the faster it rises). The more efficient the stove the less heat is wasted up the chimney and the more likely that a liner, rather than a cold void, will be what the stove requires to function correctly. “Avoid the void” is a common expression heard on stove installer training courses.