
der Todestag
death anniversary
The anniversary of the day on which a person died.
An seinem Todestag besuchen wir jedes Jahr sein Grab.
On his death anniversary, we visit his grave every year.
death anniversary / date of death
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death anniversary
The anniversary of the day on which a person died.
An seinem Todestag besuchen wir jedes Jahr sein Grab.
On his death anniversary, we visit his grave every year.

date of death
The calendar day on which a person actually dies.
Der genaue Todestag konnte erst nach der Obduktion festgestellt werden.
The exact date of death could only be determined after the autopsy.
The word is a compound of 'der Tod' (death) and 'der Tag' (day), connected by an '-es-'. So it literally means 'der Tag des Todes' (the day of death).
Der Todestag der Queen war ein weltweites Medienereignis.
The date of the Queen's death was a global media event.
The meaning depends on the context. If it is about remembrance, commemoration, or a recurring date, it means the anniversary. If it is about an investigation or a report, it means the actual day of death.
Zum 100. Todestag des Komponisten gibt es ein Sonderkonzert.
There will be a special concert for the 100th anniversary of the composer's death.
Most often, the word is used with the preposition 'an' (on), which merges with the article to form 'am'. The genitive is also very common for naming the person.
Am Todestag meines Großvaters zünden wir immer eine Kerze an.
On the anniversary of my grandfather's death, we always light a candle.
When the anniversary is meant, the verb 'sich jähren' (to mark an anniversary) is often used. For example, you say: 'Der Todestag jährt sich zum zehnten Mal.' (It is the tenth anniversary of the death.)
Nächstes Jahr jährt sich ihr Todestag zum fünften Mal.
Next year will mark the fifth anniversary of her death.
anniversary
Todestag clearly refers to the annual recurrence of the date on which someone died. Jahrestag can refer to the same date, but it usually needs an additional specification or clear context because many other events also recur annually.

Heute ist der Todestag der bekannten Schriftstellerin.
Today is the death anniversary of the well-known writer.
Heute ist der Jahrestag des Todes der bekannten Schriftstellerin.
Today is the anniversary of the death of the well-known writer.