Moment of inertia, abbreviated as I, also called rotational inertia, measures the resists or change an object has to rotational acceleration about an axis. The larger the moment of inretia the more difficult to try to get an object moving and the smaller the moment of inretia the easier of relatively easier to get an object moving.
Inertia is the tendency of an object in motion to remain in motion or an object at rest to remain at rest unless acted upon by a force. The larger the mass of an object the more resistance to change in motion than objects of a lesser mass. It is the tendency of objects to keep moving in a straight line at a constant velocity and direction forever unless acted upon by gravity or another force.
First moment of area, also called first moment of inertia, is the resistance of an object to bend around a certain axis. This is more non engineering related.
Second moment of area, also called second moment of inertia, is the resistance of an object to bend around a certain axis for a section. This is used in engineering of beams and supports.