Inelastic collision
An inelastic collision is one in which the total kinetic energy of the system decreases. Momentum is still conserved; the kinetic energy that disappears is transformed into heat, sound and permanent deformation rather than destroyed.
Almost every real collision is this kind. EK 4.4.A.3 defines it as a collision in which the total kinetic energy of the system decreases, and EK 4.4.A.4 says where the energy goes: nonconservative forces transform it into other forms instead of restoring it as kinetic energy.
Momentum is untouched by any of that. An isolated system conserves momentum whether or not kinetic energy survives, so masses and initial velocities plus one final velocity still determine the other, exactly as in the elastic case.
Inelastic does not mean the objects stick together. Sticking is the special case, a perfectly inelastic collision, where the objects leave with one shared velocity and the kinetic energy loss is the largest the momentum allows. Two carts that bounce apart weakly are inelastic as well.
Energy is not lost in the wider sense. Total energy is conserved; it simply stops being kinetic. A dented panel, a bang and warm brake pads are the missing joules, and an exam answer that says energy was destroyed will not score.
A useful check on your own work: compute the total kinetic energy before and after. If it dropped, the collision was inelastic. If it rose, you have made an arithmetic error or the problem is an explosion, where internal stored energy is released.
What is conserved in a collision sets the three cases side by side.