You're confusing yourself. A singularity is the theoretical condensing of all matter and energy in the universe into one very tiny point. Mass is not infinite at speed of light because mass is not created or destroyed (how can it be infinite?) Speed doesn't create more mass, so what the fuck are you talking about? Do you even know?
Hey dumb ass know-it-all, Einstein was talking about INERTIAL mass becoming infinite at the speed of light, you idiot!
Gravitational mass is measured by comparing the force of gravity of an unknown mass to the force of gravity of a known mass. This is typically done with some sort of balance scale. The beauty of this method is that no matter where, or what planet, you are, the masses will always balance out because the gravitational acceleration on each object will be the same. This does break down near supermassive objects such as black holes and neutron stars due to the high gradient of the gravitational field around such objects.
Inertial mass is found by applying a known force to an unknown mass, measuring the acceleration, and applying Newton's Second Law, m = F/a. This gives as accurate a value for mass as the accuracy of your measurements. When the astronauts need to be weighed in outer space, they actually find their inertial mass in a special chair.
The interesting thing is that, physically, no difference has been found between gravitational and inertial mass. Many experiments have been performed to check the values and the experiments always agree to within the margin of error for the experiment. Einstein used the fact that gravitational and inertial mass were equal to begin his Theory of General Relativity in which he postulated that gravitational mass was the same as inertial mass and that the acceleration of gravity is a result of a 'valley' or slope in the space-time continuum that masses 'fell down' much as pennies spiral around a hole in the common donation toy at your favorite chain store.
To state the answer one more time, there is
no difference between gravitational and inertial mass as far as we know.