Champagne help w/Special Club (CM,RM, RC, SR)

Trying to understand what Special Club looks like in practice with its labeling designations. Let's use Paul Bara as an example/reference point. If Paul Bara bottles a non-Special Club wine, (i.e. Brut Rose) will the wine fall under the Récoltant Manipulant designation? If so, does a Paul Bara Special Club bottling fall under another designation and which one (Coopérative Manipulant, Récoltant Coopérateur, Société de Récoltants)? I guess the core of my question is does the designation follow the producer or the specific bottle? Thank you.