die Anmerkung
remark / comment
A short spoken or written statement, remark, or comment on a specific topic.
Er erlaubte sich eine kritische Anmerkung zu dem Vortrag.
He allowed himself a critical remark about the lecture.

remark / note
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remark / comment
A short spoken or written statement, remark, or comment on a specific topic.
Er erlaubte sich eine kritische Anmerkung zu dem Vortrag.
He allowed himself a critical remark about the lecture.

The word is derived from the verb 'anmerken' (to remark / to note). The prefix 'an-' suggests that you 'attach' or add a piece of information to a topic.
Darf ich dazu etwas anmerken?
May I add something to that?
The most common combination is the phrase 'eine Anmerkung machen' (to make a remark). You can also add adjectives to describe the type of remark, e.g. 'eine persönliche Anmerkung' (a personal remark) or 'eine kurze Anmerkung' (a brief remark).
Der Chef machte zu jedem Vorschlag eine kurze Anmerkung.
The boss made a brief remark about each suggestion.
You can recognize this meaning from the context of academic or formal texts. Words like 'Fußnote' (footnote), 'Quelle' (source), 'siehe' (see), or a number directly after the word, e.g. 'Anmerkung 5' (note 5), are clear signals.
Der Autor verweist in Anmerkung 12 auf eine wichtige Studie.
In note 12, the author refers to an important study.
comment
'der Kommentar' and 'die Anmerkung' can both be a short statement about a topic. 'Kommentar' often sounds more like an opinion or reaction, for example on the internet, in a newspaper, or in program code. 'Anmerkung' usually sounds more neutral and more like a brief note or addition, especially in texts. Learners may confuse the words because you can write both about a topic. When someone is evaluating something or reacting, 'Kommentar' often fits. When someone is only adding or explaining something, 'Anmerkung' often fits.

Am Ende der Seite erklärt eine Anmerkung ein schwieriges Wort.
At the end of the page, a note explains a difficult word.
Unter dem Artikel steht ein langer Kommentar zur neuen Regel.
Under the article, there is a long comment about the new rule.