dann
then
Indicates a chronological sequence; after that, afterwards.
Zuerst putze ich die Zähne, dann gehe ich ins Bett.
First I brush my teeth, then I go to bed.

then
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then
Indicates a chronological sequence; after that, afterwards.
Zuerst putze ich die Zähne, dann gehe ich ins Bett.
First I brush my teeth, then I go to bed.

'Dann' is an adverb, not a conjunction. When it stands at the beginning of a sentence (position 1), the conjugated verb must follow directly after it in position 2 (inversion).
Wir essen jetzt zu Abend. Dann sehen wir einen Film.
We're having dinner now. Then we'll watch a film.
In 'Wenn-dann-Sätzen' (if-then sentences), 'dann' introduces the result in the main clause. It can be used for emphasis, but it is often optional and can be left out.
Wenn du Zeit hast, dann können wir uns treffen.
If you have time, then we can meet up.
'Dann' is used very frequently to order steps in an action or events in a story. It often appears in a chain with adverbs like 'zuerst' (first) and 'danach' (after that).
Zuerst die Zwiebeln schneiden, dann in der Pfanne anbraten.
First cut the onions, then fry them in the pan.
The combination 'na dann' is a very common reaction in spoken language. It expresses agreement, a conclusion, or the beginning of an action.
Die Arbeit ist fertig. Na dann, schönen Feierabend!
The work is done. Well then, enjoy your evening!
and
'und' and 'dann' can both show that something happens after something else or follows from it. 'und' connects the sentences more simply: first one thing happens, and afterwards or because of that, the other thing happens. 'dann' makes the sequence or result clearer. It often means 'after that' or 'in that case'. They can be confused because both can stand between two actions in everyday sentences. If you only want to connect things, use 'und'. If the time sequence or consequence is important, 'dann' sounds more precise.

Nach dem Gespräch schreiben wir den Bericht, dann schicken wir ihn an das Team.
After the discussion, we write the report, then send it to the team.
Die Eltern kochen heute in der Küche und decken danach den Tisch.
The parents are cooking in the kitchen today and then setting the table.