I presume you are discussing about PCB specifications and fabrications.
Yes, the base copper weight is directly related to the trace thickness. Plating thickness will be related to the copper plating thickness in e.g., plated through holes.
The base copper weight is the copper weight as it is delivered from the base material manufacturer. The plating thickness is the copper thickness added during
the plating process.
During the plating process , copper is added to inside of the holes, to build a through hole, but the plating is also added to the traces. Your final trace thickness
will be the base copper weight + the plating thickness.