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.

'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' both connect parts of a sentence. 'und' simply adds information in a sequence: both parts fit together or stand neutrally side by side. 'aber' shows a contrast or limitation: the second part does not quite fit what you would expect. The words can be confused because both can stand in the same place in a sentence. If you only want to add something, use 'und'. If you want to show a contrast, use 'aber'.

Mein Kollege wollte in der Pause anrufen, aber sein Handy war leer.
My colleague wanted to call during the break, but his phone was dead.
Im Bus saßen Lena und Tom nebeneinander.
Lena and Tom sat next to each other on the bus.