die Bemerkung
remark / comment
A short spoken or written statement with which you state, comment on, or note something.
Er machte eine witzige Bemerkung über das Wetter.
He made a funny remark about the weather.

remark
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remark / comment
A short spoken or written statement with which you state, comment on, or note something.
Er machte eine witzige Bemerkung über das Wetter.
He made a funny remark about the weather.

'Die Bemerkung' (the remark) is the noun related to the verb 'bemerken' (to notice). When you notice something and then say or write it down, you make a remark.
Er hat meine neue Frisur sofort bemerkt.
He noticed my new hairstyle right away.
When referring to a spoken statement, the verb 'machen' (to make) is often used. Typical phrases are 'eine Bemerkung machen' (to make a remark) or 'eine Bemerkung fallen lassen' (to drop a remark).
Er konnte sich eine spöttische Bemerkung nicht verkneifen.
He couldn't resist making a mocking remark.
In the meaning of 'written note', the word is often found in formal or academic texts. Prepositions like 'unter' (under), 'in' (in), or 'am Rande' (in the margin) point to this meaning.
Im Protokoll fand ich eine handschriftliche Bemerkung des Chefs.
In the minutes, I found a handwritten note from the boss.
word
'das Wort' and 'die Bemerkung' can both mean an utterance. Here, 'Wort' is more general and can mean a short statement, a speech, or even just individual words. 'Bemerkung' is usually a short comment or note about a situation. It often sounds more specific: someone says or writes something because they want to point something out. If the only important thing is that someone said something, 'Wort' fits. If it is about a short comment, 'Bemerkung' is more precise.

Beim Arzt hat der Mitarbeiter eine kurze Bemerkung in die Akte geschrieben.
At the doctor's office, the employee wrote a short note in the file.
Nach dem Streit hat sie kein Wort mehr gesagt.
After the argument, she did not say another word.