QUICK ANSWER
"Move in" is an intransitive verb phrase which is often translated as "mudarse", and "into" is a preposition which is often translated as "en". Learn more about the difference between "move in" and "into" below.
move in(
muv
ihn
)An intransitive verb phrase is a phrase that combines a verb with a preposition or other particle and does not require a direct object (e.g., Everybody please stand up.).
a. mudarse
We moved in two weeks ago and still haven't finished unpacking.Nos mudamos hace dos semanas y aún no hemos terminado de desempacar.
b. instalarse
After we move in, we're going to relax for a few days before returning to work.Después de instalarnos, vamos a relajarnos unos días antes de volver al trabajo.
a. intervenir
Police moved in to start arresting people at the demonstration.La policía intervino para comenzar a arrestar a personas en la manifestación.
into(
ihn
-
tu
)A preposition is a word that indicates the relationship between a noun and another word (e.g., He ran through the door.).
4. (time)
a. no direct translation
This refers to an idiomatic word or phrase for which there is no word-for-word translation.
Five minutes into Act II, he had a heart attack.A los cinco minutos de empezar el Acto II, sufrió un infarto.
The devaluation continued into the 1960s.La devaluación continuó hasta los años sesenta.
a. de
There is to be an inquiry into the election fraud.Van a hacer una investigación del fraude electoral.
7. (colloquial) (indicating an interest in)
A word or phrase that is commonly used in conversational speech (e.g., skinny, grandma).
a. no direct translation
This refers to an idiomatic word or phrase for which there is no word-for-word translation.
He used to be into drugs.Antes tomaba drogas.
I'm really into knitting.Me gusta mucho tejer.