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Friction is quite dissimilar to inertia though. Friction converts kinetic energy into heat. Inertia does not. Friction is dissipative, inertia is conservative. Friction acts when matter moves against matter. Inertia acts when a force is applied to matter.
Inertia is not a force, it is a property. A property which resists acceleration. It is only experienced when an actual force is applied to mass.
A good example is the traditional explanation of the gravitational well around a black hole being described as an indention in the space-time surrounding it - objects orbit because their centrifugal energy counters the force pulling them down into the indention.