
nachträglich
belated
Taking place or happening at a later point in time, after the actual event has already passed.
Herzlichen Glückwunsch nachträglich zum Geburtstag!
Happy belated birthday!
belated / subsequent
Loading your saved state.

belated
Taking place or happening at a later point in time, after the actual event has already passed.
Herzlichen Glückwunsch nachträglich zum Geburtstag!
Happy belated birthday!

subsequent
Added as a supplement or addition to something existing, often in formal or legal contexts involving contracts or documents.
Die Änderungen wurden nachträglich in den Vertrag aufgenommen.
The changes were subsequently added to the contract.
The word is made up of 'nach' (after) and a form of 'tragen' (to carry). It therefore describes something that is 'nachgetragen' (added later), meaning added or made up for later.
Die fehlenden Informationen wurden nachträglich per E-Mail geschickt.
The missing information was subsequently sent by email.
As an adverb, 'nachträglich' usually stands in the middle of the sentence, often after the conjugated verb and temporal information. It indicates that the action of the verb takes place later than the main event.
Wir haben die Dokumente erst gestern nachträglich erhalten.
We only received the documents subsequently yesterday.
In this meaning, 'nachträglich' is very often used for belated congratulations or apologies. Typical phrases are 'nachträglich alles Gute wünschen' (to wish someone all the best belatedly) or 'sich nachträglich entschuldigen' (to apologize afterward).
Ich möchte mich nachträglich für mein Verhalten entschuldigen.
I would like to apologize afterward for my behavior.
This meaning is often found in formal, technical, or legal contexts. Signal words are verbs like 'ändern' (to change), 'einbauen' (to install/build in), 'genehmigen' (to approve), or nouns like 'Vertrag' (contract), 'Protokoll' (minutes/record), and 'Gebäude' (building).
Der Balkon wurde nachträglich an das Haus angebaut.
The balcony was subsequently added to the house.
retroactive
Both words can describe a change decided on later. „Nachträglich“ means that something is added or changed only later. „Rückwirkend“ additionally means that this change applies to a period in the past.

Die Parteien haben die neue Vergütung nachträglich in den Vertrag aufgenommen.
The parties subsequently added the new remuneration to the contract.
Die neue Vergütung gilt rückwirkend ab dem Beginn des Vertrags.
The new remuneration applies retroactively from the beginning of the contract.