Nalla,  If you are working to ASME Sect. IX,  QW-361.1 covers variables for Automatic Welding (welding performed by an Operator).   QW-350 covers variables for welders.   There are different requirements for operators versus welders.  QW-361.1 (b) states that for automatic welding "a change in the welding process" is an essential variable, so you would definitely need to qualify the operator on both GTAW and FCAW processes.   QW-306 allows an operator to qualify on two separate test coupons or on one test coupon using both processes.
Regards, Sol