hinein
into
Expresses movement from outside to inside a room, container, or area. The perspective is outside the destination.
Schau mal durch das Fenster ins Zimmer hinein.
Take a look through the window into the room.

in / into
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into
Expresses movement from outside to inside a room, container, or area. The perspective is outside the destination.
Schau mal durch das Fenster ins Zimmer hinein.
Take a look through the window into the room.

'Hinein' (in/into) is a directional adverb made up of 'hin' and 'ein'. 'Hin' describes movement away from the speaker, and 'ein' means into something.
Er ging langsam in die dunkle Höhle hinein.
He slowly went into the dark cave.
'Hinein' (in/into) can be combined with many verbs to form a new separable verb, e.g. 'hineingehen' (to go in), 'hineinschauen' (to look in). In a main clause, the prefix goes at the end; in a subordinate clause, the verb stays together.
Bitte gehen Sie schon mal ins Wartezimmer hinein.
Please go on into the waiting room.
You can recognize the spatial meaning (m01) from verbs of movement and location information. You can recognize the temporal meaning (m02) from time expressions such as 'Nacht' (night), 'Tag' (day), or 'Zukunft' (future).
Er kletterte vorsichtig in den Brunnen hinein.
He climbed carefully into the well.
'Hinein' (in/into) is often used together with a prepositional phrase that describes the destination of the movement more precisely. The adverb 'hinein' then reinforces the direction.
Die Katze sprang mit einem Satz in den Karton hinein.
The cat jumped into the box in one leap.
in
'in' and 'hinein' can both express movement inward. 'in' is a preposition and is used with a noun, for example 'in den Raum' (into the room) or 'in die Tasche' (into the bag). 'hinein' is an adverb and emphasizes movement from outside to inside. It can stand on its own when it is clear where the movement is going, or it can be used additionally with a place. Learners confuse the words because both occur with movements into an area. A practical rule: if you need a noun directly after it, often use 'in'. If you want to emphasize the direction inward, 'hinein' fits.

Als es kalt wird, gehen wir schnell hinein.
When it gets cold, we quickly go inside.
Das Kind legt den Ball in die Kiste.
The child puts the ball into the box.