It is not so much their differentiation, as it is their identity, that is extraordinary.
Consider the following. Inertial mass as defined describes an object's resistance to forces that attempt to change its motion. Described in Newton's second law,
F = d/dt(momentum) = m * dv/dt
for a mass that does not change with time.
The inertial mass can therefore be seen as the scaling factor between the (net) force acting on an object, and the resulting change in motion as effected by the force.
The gravitational mass, on the other hand, describes the magnitude that a certain object is affected by a gravitational field. Looking at it in either the form
F = GMm/(r^2) = gm
where G is the gravitational constant, and M is the mass of the other (large) mass. In that sense then, if we were to consider g as being a quantity intrinsic to the gravitational field (rather than the object), the gravitational mass m then becomes a scaling factor between the strength of the gravitational field, and the force experienced by an object due to the influence of the gravitational field.
There is little theoretical work (and none legitimate) during Newton's time that can explain why these two scaling factors should be the same. Considering both as intrinsic properties of the object, why should the tendency of an object to be affected by gravitational fields, be related in any way to the resistance of the object to changes in its motion due to external forces? The equivalence of the two values (equivalence principle) is therefore something that needs to be experimentally verified, and the search for a difference between the two has been ongoing since his time.
As an aside, it is perhaps important to note that other forces of attraction and repulsion (as understood at that time) all have their own unique scaling factors. Be it the charge of particles for electrostatic forces, or the magnetisation strength of certain materials for magnetic forces, it does not seem like any correlation exists between them or with the mass property of the object. The uniqueness of these two values stands out.
Taking a closer look at the two formulas:
F = m * dv/dt | F = m * (GM/(r^2))
The greater the resistance of an object is to being moved, the stronger is the attractive force exerted by an object on neighbouring objects to pull them towards it. Now, consider a ball placed on a taut bedsheet. The deeper the ball sinks into the bedsheet, the harder it is to move the ball. But, with a deeper depression created by the ball, the tendency for neighbouring balls affected by the depression to roll towards the main ball increases. This is a really, really crude way to think about general relativity, but I suppose it could pass off as a tiny bit of inspiration.