der Hochzeitstag
wedding anniversary
The anniversary of a marriage, on which a couple celebrates the continuation of their marriage.
Wir feiern heute unseren zehnten Hochzeitstag.
We are celebrating our tenth wedding anniversary today.

wedding anniversary / wedding day
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wedding anniversary
The anniversary of a marriage, on which a couple celebrates the continuation of their marriage.
Wir feiern heute unseren zehnten Hochzeitstag.
We are celebrating our tenth wedding anniversary today.

The word is a compound of 'Hochzeit' (wedding) and 'Tag' (day), connected by the linking '-s'. It literally means 'the day of the wedding'.
Wir haben unseren Hochzeitstag mit einem besonderen Abendessen gefeiert.
We celebrated our wedding anniversary with a special dinner.
In the sense of an anniversary, the word is often combined with the verb 'feiern' (to celebrate) and ordinal numbers or special names.
Nächstes Jahr feiern wir unseren 25. Hochzeitstag, die Silberhochzeit.
Next year we will celebrate our 25th wedding anniversary, our silver wedding anniversary.
When congratulating someone, you use the preposition 'zu' with the dative. The fixed expression is: 'jemandem zum Hochzeitstag gratulieren' (to congratulate someone on their wedding anniversary).
Ich möchte euch herzlich zum Hochzeitstag gratulieren!
I would like to warmly congratulate you on your wedding anniversary!
The meaning 'the day of the wedding ceremony' is often made clear by the tense of the verb. If you are speaking in the simple past or present perfect about a specific day in the past, the original day is often meant.
Unser Hochzeitstag war der schönste Tag in meinem Leben.
Our wedding day was the most beautiful day of my life.
wedding / heyday
'die Hochzeit' and 'der Hochzeitstag' are closely connected, but they are not the same. 'Hochzeit' means the celebration or ceremony where two people get married. 'Hochzeitstag' can be the exact calendar day on which the wedding takes place. Very often, however, it means the wedding anniversary that a couple celebrates every year. The confusion arises because both words contain the word 'Hochzeit'. When you are talking about the event, you say 'Hochzeit'. When you are talking about the day or the anniversary, you say 'Hochzeitstag'.

Zum Hochzeitstag schenken wir unseren Eltern ein gemeinsames Foto.
For their wedding anniversary, we are giving our parents a photo of them together.
Die Hochzeit meiner Schwester war sehr schön und dauerte bis Mitternacht.
My sister's wedding was very beautiful and lasted until midnight.