When are the phrases in motion and in movement used? In motion is the most popular form based on a Google search, but in movement still has 3 080 000 results.
It might be totally wrong, but I'd like to share my understanding of the two:
Movement: moving from one place to another
Motion: not standing still
In that sense, in motion might be regarded as opposite of stationary while in movement could indicate something or somebody is in the process of moving from place A to place B.
Intuitively, in motion brings me back to high school physics class; in movement just reminds me that some political or social movement is taking place.
According to etymonline both movement and motion trace their origin to L. movere "move, set in motion".
Different senses acquired later were, for:
motion: The verb sense in parliamentary procedure first recorded 1747; with meaning "to guide or direct by a sign, gesture, movement" it is attested from 1787.
movement: In the musical sense of "major division of a piece" it is attested from 1776; in the political/social sense, from 1828.
The phrase "in motion" has been much more common since it is used in idiom "set in motion", which is used to say "to give an impulse (impetus) to".
The phrase is much more common:
To say that something is "in motion", generally speaking, means that it is moving (lit. or fig.), and to say that something is "in movement" would mean that it is a part of a movement. So, if you want to say that something is moving, do not say that is "in movement"; that will most likely be confusing.
On the other hand, as nouns, the two words are almost interchangeable and even in physics it is hard to find distinguishing definitions, however certain terms will consistently use motion vs movement, where they can not be interchanged e.g. brownian motion vs particle movement. Also, in physics the term motion is used more frequently.
Overall a movement implies some sense of complexity and a motion is, usually, simpler and regular in some way. Also, I would prefer motion for a single instance of some action and movement if I want to talk about generalized idea.
"In motion" is a phrase used as an adjective to describe a thing that is moving. Here you would never separate "in" and "motion", they go together as a singular phrase.
He caught the ball while it was still in motion.
A toddler is perpetually in motion; he doesn't sit still for an instant.
Here you could easily substitute the word moving.
There's nothing special about the phrase "in movement". Sometimes the two words appear next to each other, but they are not really used together as a singular phrase. You could have:
A lesson in movement.
Functional imaging in movement disorders.
But this is really just:
A lesson in (some subject). e.g. A lesson in geography.
Functional imaging in (some kind of) disorders. e.g. Functional imaging in mood disorders.
The Google NGrams results for 'in movement' show a whole bunch of occurrences like this.