
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.

note / comment
A written comment, note, or annotation added to a text or document in order to explain or supplement something.
Unter dem Vertragstext stand die Bemerkung, dass alle Änderungen schriftlich erfolgen müssen.
Under the contract text was the note that all changes must be made in writing.
'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
Both words can refer to a short utterance. A Bemerkung is specifically usually a brief comment or observation, while Wort can also mean a longer speech and is often used for a contribution in fixed conversational expressions. Use Bemerkung for an incidental comment and Wort for your own contribution to a conversation.

Seine kurze Bemerkung zum Wetter brachte alle zum Lachen.
His brief comment about the weather made everyone laugh.
Ich möchte zu diesem Thema noch ein Wort sagen.
I would like to say a few words on this topic.