An object is in motion when
a. you observe the object move.
b. the object’s speed increases.
c. the object’s displacement is greater than the distance traveled.
d. the object changes position relative to a stationary reference point.

When an object changes its position relative to something else,
you look at and say that it's in motion.

Somebody standing next to you could just as well watch the exact
same situation, and notice that the other thing changed its position
relative to your object, and say that the other thing is in motion.

Who is correct ? 
Both of you are.

Which thing is really moving ?
There's no such thing as really moving.
Motion is always relative to something else.

When you come out of the bathroom, walk to your seat
and sit down, do you stop moving ?
What if your seat is in row-27 of the airliner you're on,
flying 450 miles per hour at 27,000 feet ?