Dynamics is the extension of statics by inertial force F_inert=-dp/dt (minus!). A fundamental law of statics is the equilibrium of forces.
Sum over all external forces = 0
(Sum over all internal forces = 0)
Thus, a fundamental law of dynamics reads
Sum over all external plus inertial forces = 0,
see Newton's 2nd axiom.
Example 1, spring: If you press or stretch a spring of its equilibrium state to another position, it exerts a real counter-force of equal strength but opposite direction upon you, cf. Newton's 3rd axiom -- no fictitious forces involved.
Example 2, car changing direction: The car behaves as if a centripetal force acts upon it. Correspondingly, there is a counter-force acting in opposite direction, the centrifugal force. This is really felt by all being moving together with the car. -- For all outside the car, there is no change of motion and hence no counter-reaction. For this, centrifugal force is not a fictitious force.
Example 3, winds: Since the Earth's body and its atmosphere are not tightly bound to each other, the Earth's body moves relative to its atmosphere. For this, a cloud, which is at rest relative to the fixed stars (assumed to build an inertial system), moves relative to the Earth, although there is no (net) force acting upon it. From the point of view of a point fixed on the Earth's surface, the motion of the cloud relative to it is explained by a fictitious force. This fictitious force just compensates for the apparent (!) inertial force corresponding to the apparent (!) motion of the cloud.
Summa summarum, fictitious forces are forces which appear when changing from an inertial frame to a non-inertial one. Unfortunately, this is not always properly described in the literature.
Hope this helps -- if not, say it :-)