indeed / actual
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indeed / really
Confirms that something is truly the case or is the case in reality. It is used to emphasize a fact or express surprise.
Ich dachte, er scherzt, aber er hat es tatsächlich getan.
I thought he was joking, but he actually did it.
actual
As an adjective, it describes something as factual, real, or corresponding to the facts.
Die tatsächlichen Kosten waren viel höher als erwartet.
The actual costs were much higher than expected.
The word is derived from 'die Tatsache' (the fact), which means 'fact'. So 'tatsächlich' (indeed/really/actual) literally means 'corresponding to the facts' or 'like a fact'.
Die tatsächliche Situation ist komplizierter, als sie scheint.
The actual situation is more complicated than it seems.
'Tatsächlich' means 'in fact' or 'really' and confirms something. Don't confuse it with the English 'actually', which often introduces a correction or contrast and is usually translated as 'eigentlich'.
Er sieht jung aus, aber er ist tatsächlich schon über 50.
He looks young, but he is actually already over 50.
'Tatsächlich' can be used as an adverb (unchanging) or as an adjective (changing). As an adverb, it modifies the whole sentence or a verb. As an adjective, it stands before a noun and is declined.
Er hat den Job tatsächlich bekommen. (Adverb)
He actually got the job. (Adverb)
so / therefore
Also and tatsächlich can both confirm an assumption. Also indicates that the confirmation was inferred from previous clues or information. Tatsächlich emphasizes directly that something is the case in reality, often contrary to expectations.
Die Kamera zeigt, dass Paul gestern tatsächlich hier war.
The camera shows that Paul was indeed here yesterday.
Die Spuren passen zusammen: Paul war also gestern hier.
The clues fit together: so Paul was here yesterday.
