Gravitational Tides
Look closely at the gravitational
force acting on a moon as it orbits its planet:
If we subtract the center of mass force, we see the differential
force acting on it:
So gravity "stretches"
and "squashes" a moon!
Let's look at this mathematically. The force of gravity
is:
So the differential force
(also called the tidal force) across
a distance dr is
Note that

the tidal force is proportional to the mass of the primary
(M)

the tidal force is inversely proportional to the distance
cubed.
Note also that it works both ways  the moon also stretches
the planet!
Why is it called a tidal force?
What is stronger on the Earth, the tidal force from the
moon or the tidal force from the Sun?
So the moon exerts a stronger force, but the Sun's tidal
force can be significant. Hence the concept of spring
tides and neap tides:

Spring Tides: Sun
and Moon in alignment; tidal forces add. Big
tides!

Neap Tides: Sun
and Moon 90 degrees apart; tidal forces counteract. Small
tides.
Remember: Tides are not merely a water effect! The Earth's
surface also has tidal bulges, about 10cm in height. And the moon has an
even greater tidal bulge  20m high.
Thought experiment: What
happens when you keep squeezing and stretching a piece of silly putty? What
does this have to do with tides?