Let's assume that we have a person sitting on a bus. Suddenly the driver applies brakes, such that the direction of acceleration is opposite to that of motion.If the person draws the Free body diagram of himself with respect to himself, the direction of the pseudo force will be in the direction of the motion and this is what is pulling the person forward. So isn't this Pseudo force, the inertia that we talk about.
You are right. The cause of pseudo force is inertia. Let me elaborate. Pseudo forces are the forces which do not actually exist but are added to make Newtons equations hold. Here in this case, from frame of reference attached to earth, there is actually no force acting on the person in horizontal direction. But in fact there is absence of force which will decelerate the person along with decelerating bus. So due to inertia, person keeps moving. But in frame of reference of bus (which is no more inertial), person is accelerated in forward direction. So to make Newtons equations consistent in that frame, we add Pseudo force. But from earth's frame, it's just the inertia.