
schuldig
guilty
Bearing responsibility for a moral or legal wrongdoing or a crime.
Das Gericht sprach den Angeklagten des Diebstahls schuldig.
The court found the defendant guilty of theft.
guilty / owing
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guilty
Bearing responsibility for a moral or legal wrongdoing or a crime.
Das Gericht sprach den Angeklagten des Diebstahls schuldig.
The court found the defendant guilty of theft.

to owe someone something
To be obligated to pay someone back money or provide some other service in return.
Ich bin dir noch zwanzig Euro für das Abendessen schuldig.
I still owe you twenty euros for dinner.

to owe someone something
In a figurative sense, to be obligated to give someone thanks, an explanation, or a favor.
Nach all seiner Hilfe war sie ihm eine Erklärung schuldig.
After all his help, she owed him an explanation.
'Schuldig' (guilty / owing) is the adjective corresponding to the noun 'die Schuld' (guilt / debt). Since 'die Schuld' can mean both 'wrongdoing' and 'debts', the adjective 'schuldig' also has these two main meanings.
Er hat seine Schulden bezahlt und ist jetzt nichts mehr schuldig.
He has paid his debts and doesn't owe anything anymore.
In legal language, the crime for which someone is convicted is often stated using the genitive. This construction is very formal.
Der Angeklagte wurde des Betrugs schuldig gesprochen.
The defendant was found guilty of fraud.
When you owe someone something, the sentence structure is fixed: the person who owes something is in the nominative, the person to whom something is owed is in the dative, and the thing or amount is in the accusative.
Ich bin dir noch eine Erklärung schuldig.
I still owe you an explanation.
If 'schuldig' (guilty / owing) stands alone or with 'an' (+ dative), it usually means 'morally or legally responsible'. If it appears with a person in the dative and a thing in the accusative, it means 'to owe someone something'.
Sie fühlt sich schuldig, weil sie nicht geholfen hat.
She feels guilty because she didn't help.
guilt / debt
With „schuld sein an“, you say who or what caused a negative event. „Schuldig“ describes a person who has committed a moral or legal wrongdoing. „Schuld“ is therefore often appropriate for an accident, while „schuldig“ is used for a wrongdoing that is being judged.

Das Gericht erklärte Mara für schuldig, weil sie fremdes Eigentum absichtlich zerstört hatte.
The court found Mara guilty because she had intentionally destroyed someone else’s property.
Mara ist schuld daran, dass die Vase beim Spielen zerbrach.
Mara is to blame for the vase breaking while they were playing.