What's the difference between dlatego and zatem?

I sometimes attempt to write 'zatem' instead of 'dlatego' and I always seem to be corrected to write 'dlatego' instead. Thanks in advance!

'Zatem' is a pretty old-fashioned / archaic version (could be used in contemporary literature though). "Dlatego" is much more common in everyday Polish language, so it's the preferred version ;)

'Zatem' is not a precise synonym of 'dlatego'. 'Zatem' is quite often used in questions replacing the word 'więc' which seems to be much more colloquial than 'zatem'. Here are several contemporary examples from wirtualna polska.pl :

- Czy zatem w dłuższej perspektywie Brexit - paradoksalnie - może wręcz wzmocnić Unię Europejską?

- Według ks. Zielińskiego zamach w Barcelonie to kara za rozwiązłość. Czy zatem uderzenie pioruna w katedrę w Gnieźnie to kara za pedofilię księży? - zapytała na Twitterze Joanna Senyszyn.

- Zatem kierując się swoją znajomością szefa MON sądzi pan, że Antoni Macierewicz naprawdę wierzy w zamach smoleński?

In the first examples, I could easily replace 'zatem' with 'więc' or 'dlatego'. In the second, I would do it with 'więc', but rather reluctantly with 'dlatego'. In the last one I could replace 'zatem' with 'tak więc' or 'a więc' since we do not start a sentence with 'więc' alone. But I would never use 'dlatego' there.