
aber
but
Introduces a contrast or limitation to something said previously.
Der Film war gut, aber sehr lang.
The film was good, but very long.
but
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but
Introduces a contrast or limitation to something said previously.
Der Film war gut, aber sehr lang.
The film was good, but very long.

really
Used as a particle to emphasize a statement, often to express surprise, indignation, or agreement.
Das ist aber eine schöne Überraschung!
That really is a nice surprise!

but
After a pause or interruption, introduces the return to the actual topic.
Aber um auf deine ursprüngliche Frage zurückzukommen: Ich glaube nicht, dass das funktioniert.
But to come back to your original question: I don't think that will work.
'Aber' (but) belongs to the conjunctions that have no influence on word order. When it connects two main clauses, it stands in 'position 0' and the verb of the second clause follows in position 2.
Ich würde gerne mitkommen, aber ich habe leider keine Zeit.
I would like to come along, but unfortunately I don't have time.
When 'aber' (really) is used for emphasis, it is a particle and does not stand at the beginning of the sentence. It typically stands after the verb and emphasizes a quality or feeling, often in an exclamation.
Du kannst aber gut kochen!
You really can cook well!
In the meaning 'back to the topic', 'aber' (but) is used to steer a conversation back to the original point after a digression. This is typical of spoken language.
Das war also mein Urlaub. Aber, was wolltest du mich eigentlich fragen?
So that was my vacation. But what did you actually want to ask me?
and
Und and aber can connect two statements that are valid at the same time. Aber explicitly marks the contrast between them; und merely joins them, so any surprising tension comes from the content alone. Choose aber when the contrast should be clearly emphasized.

Die Aufgabe ist schwierig, aber Lisa löst sie schnell.
The task is difficult, but Lisa solves it quickly.
Die Aufgabe ist schwierig, und Lisa löst sie schnell.
The task is difficult, and Lisa solves it quickly.