rein
clean
Clean, without dirt or stains.
Nach dem Putzen war die ganze Wohnung wieder rein.
After cleaning, the whole apartment was clean again.

pure / in
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clean
Clean, without dirt or stains.
Nach dem Putzen war die ganze Wohnung wieder rein.
After cleaning, the whole apartment was clean again.

The word 'rein' is very versatile. It can be an adjective ('reine Wäsche' = clean laundry), an emphasizing adverb ('reiner Zufall' = pure coincidence), or a colloquial particle for movement inward ('komm rein!' = come in!). You can recognize its function from the word order and the context.
Das ist reines Gold.
That is pure gold.
As a short form for 'herein' (in here) or 'hinein' (into), 'rein' is very common in spoken language. It behaves like a separable prefix and appears at the end of the sentence or alone as a command.
Darf ich kurz reinkommen?
May I come in for a moment?
As an adverb, 'rein' means something like 'only' or 'exclusively' and emphasizes a noun. It stands directly before the noun it intensifies. Typical expressions are 'reiner Zufall' (pure coincidence), 'reine Zeitverschwendung' (a complete waste of time), or 'aus reiner Freundlichkeit' (out of pure kindness).
Dass wir uns im Urlaub getroffen haben, war reiner Zufall.
The fact that we met on vacation was pure coincidence.
In the meaning 'unmixed' or 'pure', 'rein' often describes materials. Common combinations are 'reine Baumwolle' (pure cotton), 'reines Gold' (pure gold), or 'reiner Alkohol' (pure alcohol).
Der Pullover ist aus reiner Schurwolle.
The sweater is made of pure new wool.
The fixed expression 'etwas ins Reine schreiben' means to create a clean, error-free final version of a text. The object stands between 'ins' and 'Reine'.
Bis morgen muss ich meinen Aufsatz ins Reine schreiben.
I have to write up my essay neatly by tomorrow.
only
'nur' and 'rein' can both express that something is meant exclusively in that way. 'nur' is the normal and very common word here. 'rein' is used more in fixed or suitable phrases, for example 'rein beruflich' (purely professional), 'rein zufällig' (purely by chance), or 'rein privat' (purely private). It often sounds a little more emphatic: it really is about nothing else. They can be confused because 'rein' also has other meanings, for example 'clean' or, colloquially, 'in / into'. If you simply want to limit an amount or thing, 'nur' is usually more natural.

Ihre Entscheidung war rein praktisch, weil der andere Weg am Abend zu lang war.
Her decision was purely practical, because the other route was too long in the evening.
Im Büro geben wir nur den Teamleitern die neuen Pläne zur Vorbereitung.
At the office, we give the new plans only to the team leaders for preparation.