Give me the difference between a perfectly inelastic collision &

an inelastic collision.

Perfectly elastic looks like Mv + mV = Mw + mW
Perfectly inelastic looks like Mv + mV = (M + m)w

Where M and m are two colliding masses at v and V initial velocities, with w and W as post collision velocities. Both equations depict the conservation of momentum where momenta before the collision equals momenta after the collision. The major difference is that the two masses fly apart in perfect elastic, but stick together in perfect inelastic.