The short answer is neither!
Read the Stanford lecture notes cited by Capt. Peter (not really dated) and you will get a lot of information on how local lift coefficient varies across the span.
The total lift is an integration of all these bits.
When folks talk about wing area they generally mean the REFERENCE area, which can be anything the designer chooses.
The OVERALL lift coefficient is then the integral of the local lifts divided by this reference area.
Therefore, so long as you are consistent, local Cl has to come from detailed aerodynamic calculations, but CL is a global average