When gravitational motion of test objects are studied, two distinct concepts of mass are invoked in principle, namely, inertial mass and (passive) gravitational mass. If inertial mass and gravitational mass are quantities, then according to the definition of ``quantity'' available in the standard literature of metrology, there need to be specific units corresponding to inertial mass and gravitational mass. The possibilities of such definitions and the associated obstacles of reason are discussed. A recent classification of ``kilogram'' as a unit of inertial mass, that depends on the realization of kilogram through atom count method involving the use of matter wave interferometers, is critically analyzed. The process of reasoning that leads to such a classification is misleading because the equivalence between inertial mass and gravitational mass is an implicit assumption, in the process, both at the macroscopic level (mass measurement of silicon sphere) and the microscopic level (mass measurement of silicon atom with atom wave interferometers) resulting in no a priori distinction between inertial mass and gravitational mass in the concerned literature. Further inquiry reveals a crucial, but hitherto unexplained, difference between the working principles of neutron wave interferometers and atom wave interferometers. In neutron wave interferometers, the universal free fall of neutrons is attributed to the equality of inertial mass and gravitational mass, whereas in atom wave interferometers the distinction between inertial mass and gravitational mass is not made in the first place and universal free fall of atoms is attributed to either mass difference of the different species of atoms or different energy states of the same species of atom. Such observations result in the recognition of different {it types} of universal free fall that are studied in the literature which, however, has hitherto not been recognized assertively.