Control Plane (Routing Engine, Supervisor Engine) and Data Plane (Forwarding Plane, Forwarding Engine, Switch Fabric), in routing / switching technology always hard to explain the difference.
In new architecture of routing/switching hardware (router / L3 switch), we always found control plane module an data plane module attach, or maybe there is always routing engine and ASIC processor in one box router/switch.
Control Plane have role to take responsibility handle routing processing, from route update, exchange routing information, exchange label, update cost/weight in routing path and make routing table/routing cache. it’s usually consist of high power cpu to handle all the routing calculation.
Data Plane or Forwarding Plane have role to take responsibility handle forwarding traffic/packet based on label and lookup the routing information from routing table/cache, because of this large packet handle an ASIC processor needed to do packet forwarding.