rausgehen
to go outside
To move from an enclosed space, such as a building or room, to the outside.
Bei dem schönen Wetter müssen wir einfach rausgehen.
With the weather this nice, we simply have to go outside.

to go out
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to go outside
To move from an enclosed space, such as a building or room, to the outside.
Bei dem schönen Wetter müssen wir einfach rausgehen.
With the weather this nice, we simply have to go outside.

'Rausgehen' is a separable verb. The prefix 'raus-' goes at the end in a main clause, while in a subordinate clause and in the infinitive with 'zu', it remains attached to the verb.
Wir gehen heute Abend nicht raus.
We are not going out tonight.
The prefix 'raus-' is the colloquial and very common short form of 'heraus-'. In most everyday situations, 'rausgehen' is used instead of 'herausgehen'.
Komm, wir gehen raus in den Garten!
Come on, let's go out into the garden!
Whether 'rausgehen' means simply 'nach draußen gehen' (to go outside) or 'sich amüsieren' (to have fun/go out) depends on the context. Time expressions like 'am Abend' (in the evening), 'am Wochenende' (on the weekend), or places like 'in eine Bar' (to a bar) point to the meaning 'ausgehen' (to go out).
Lass uns am Samstagabend zusammen rausgehen und tanzen.
Let's go out together on Saturday evening and dance.
When it is about stains, the subject of the sentence is the stain itself. The construction is typically '[Fleck] geht aus [Kleidungsstück] raus' ([stain] comes out of [item of clothing]).
Der Kaffeefleck geht hoffentlich beim Waschen wieder raus.
Hopefully the coffee stain will come out again in the wash.
Similar to the meaning with stains, in this meaning the subject is the message or item that is being sent out. The person sending it is often not mentioned.
Die Einladungen für die Hochzeit sind letzte Woche an alle Gäste rausgegangen.
The wedding invitations went out to all the guests last week.
out
'raus' and 'rausgehen' are closely related because both can have to do with movement to the outside. But 'raus' is an adverb and usually needs another verb or is used with 'sein': 'Ich gehe raus' (I'm going out) or 'Das Buch ist raus' (the book is out / released). 'rausgehen' is itself a verb and describes the action of someone going outside. They can be confused because 'raus' is often part of 'rausgehen'. In practical terms: if you mean the action, use 'rausgehen'; if you only mean the direction or the state, 'raus' fits.

Wir gehen heute Abend noch rausgehen, wenn das Wetter gut bleibt.
We're going to go out again this evening if the weather stays good.
Nach dem Essen gehe ich kurz raus.
After eating, I'm going outside for a bit.