Inertia is the tendency of an object at rest to remain at rest until acted upon by some outside force or agency.
Gravity is the (postulated) attractive force exerted by mass on its environment. It is thought that this force is exerted via the agency of a massless (?), 'force carrying' particle: the graviton. There are, however, serious problems with the present model of gravity. In order to integrate empirical observations of how the Unverse actually behaves - gravitationally - with the current model theorists have had to introduce two new phenomena into the equation: dark matter and dark energy. If the current model needs - at sometime in the future - to be re-jigged yet again then theorists will have to look at ditching it altogether.
However, if anyone is interested in reading a theory that explains all phenomena - a grand unified theory that unites all forces under one Universal Law - please follow this link:
The laws of motion are similar/related to the inertial laws. A moving object will continue to move: at constant acceleration, until acted upon by some outside force or agency. A moving object has more mass than an object at rest because it posses both inertia and motion.
The important thing to remember about motion is that everything that exists is on the move. Nothing stands still. Everything is moving in relation to everything else.
You could - in fact- define existence itself, as being nothing more than motion. If it moves it exists - it exists because it moves. Follow that link to find out more.