Isnt a mass defined as mass whether it's in an inertial field or non inertial field?

Question

Doesnt mass follow the same rules in gravitational containment or in free space?

Answer 1

Mass is always mass in any situation. You can´t change the mass, you only can change some properties of the mass, such as, weight (according the gravity), quantity of cinetic energy (accordind the velocity of the mass), etc. But the mass is always the same mass!!!

Answer 2

mass is mass. Mass causes 'weight' in an inertial field. As for rules if we don't wander into relativity... then yes F=ma