All you really need to know is that in elastic collision, kinetic energy is conserved, so you can use 1/2 mv^2 = ke. In inelastic collisions, kinetic energy is not conserved, so you need to use m1v1 = m2v2. The rest of the table goes through partial elastic/inelastic and how kinetic energy compares.
Another thing is that you can not go wrong by using m1v1 = m2v2 because momentum is always conserved. It's simply a longer problem to do because momentum is a vector so you need to account for all the rules of vector addition/subtraction. KE is nice because it's a scalar, thus direction doesn't matter.