Is this inertia?

Is the force called inertia when a car hits a wall/ stationary object and the person is thrown forward.

Is it the same force when a car accelerates forward and the passengers are pushed backwards into their seats.

Yes.

As I remember the, law of inertia stated that a body at rest continues to be at rest until a force acts upon it. Also, a body at motion continues to be in motion until a force acts upon it.

In the first case, when a car hits a wall and the person is thrown forward the person is relatively at motion with the car. When car comes to rest, the body resists to come to rest and continues to be in motion, thus it moves forward.

In the second case, when a car accelerates forward and the passengers are pushed backwards into their seats, both of them are at rest. When the car accelerates, the body resists to be in motion, thus it continues to be at rest and is pushed back.

yes but inertia IS NOT A FORCE........ but both the statement has one thing in common...................that every massive body has a property called inertia. which opposes the change in state of motion..................When car is moving, the driver and the pessengers are also moving along it.......but when car stops suddenly due to external force, the driver and pessengers keep moving due to their property of inertia and thats why they are thrown forward.........Simillar thing happens in the next case

I took these from the source listed below. Maybe that will help explain it.

The more inertia which an object has, the more mass it has. A more massive object has a greater tendency to resist changes in its state of motion.
A common physics demonstration relies on this principle that the more massive the object, the more that object tends to resist changes in its state of motion. The demonstration goes as follows: several massive books are placed upon a teacher's head. A wooden board is placed on top of the books and a hammer is used to drive a nail into the board. Due to the large mass of the books, the force of the hammer is sufficiently resisted (inertia). This is demonstrated by the fact that the hammer blow is not felt by the teacher. (Of course, this story may explain many of the observations which you previously have made concerning your "weird physics teacher.") A common variation of this demonstration involves braking a brick over the teacher's hand using the swift blow of a hammer. The massive bricks resist the force and the hand is not hurt. (CAUTION: do not try these demonstrations at home.)

exactly, it is due to inertia, according to law of inertia, if a body is moving or stationery, it will not change its position until a force is applied on it. Due to external force of wall or acceleration of a car, body oppose this force and you feel like this.