A collision is simply when there are two objects involved,
at least one of them is moving, and they bump together.
An elastic collision is one in which no kinetic energy is lost,
so the total kinetic energy after the collision is the same as
it was before.
In real life on Earth, there's always some friction during the
collision, and friction robs kinetic energy, so no collision is
ever perfectly elastic. Whenever you get a school Physics
problem that involves a collision, the problem will always tell
you when you're supposed to assume that it's elastic. When
you see that, it's a big green flag that tells you that you can
probably make a bee-line straight to the answer if you just
write down the kinetic energy before, the kinetic energy after,
and set them equal.
Your example:
You throw a tennis ball to your dog.
A very complicated situation !
First, when is there a collision ?
-- If the ball bounces before the dog gets it, there's a collision
between the ball and the ground.
Kinetic energy is gained as gravity pulls the ball down to the
ground. Kinetic energy is lost to friction in the bounce, when
all the little hairs on the tennis ball scrape against concrete or
blades of grass. Energy is also lost because the ball smooshes
against the ground and then springs back to being a ball. The
squeezing and stretching of the rubber swallows some energy.
That's why a ball never bounces back as high as you drop it from.
-- Another collision when the dog snatches the ball out of the air
and it sticks in his mouth.
If the dog was hanging from a rope or a harness and was free to
swing, this might actually be almost an elastic collision. After he
caught the ball, the dog would swing with all the kinetic energy
that he got from the ball.
But he's not free to swing, and he doesn't go anywhere after he
catches the ball. What happened to the kinetic energy of the ball ?
It was immediately absorbed by the dog's neck muscles, and there's
none left. So the kinetic energy after that collision is zero, and the
collision is definitely not elastic.
Whenever you need to decide, look at the kinetic energy before
and after. Remember, kinetic energy of each moving object is
(1/2) x (mass) x (speed squared).
If the total kinetic energy of all moving objects is the same before
and after the collision, then the collision was elastic.