
auffallen
to stand out
To attract attention, to be noticed, often because of a special feature or behavior.
Mit ihrem roten Mantel fällt sie in der Menge sofort auf.
With her red coat, she immediately stands out in the crowd.
to stand out / to notice
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to stand out
To attract attention, to be noticed, often because of a special feature or behavior.
Mit ihrem roten Mantel fällt sie in der Menge sofort auf.
With her red coat, she immediately stands out in the crowd.

to notice
To be noticed or perceived by someone. Used impersonally with a dative object to express that someone becomes aware of something.
Ist dir aufgefallen, dass das Licht im Flur nicht funktioniert?
Did you notice that the light in the hallway isn't working?
'Auffallen' (to stand out / to notice) is a separable verb. The prefix 'auf' comes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Sein neues Auto fällt sofort auf.
His new car stands out immediately.
This verb is very often used with a person in the dative to express who notices something. The structure is: [person in the dative] fällt [thing in the nominative] auf.
Mir ist seine neue Frisur sofort aufgefallen.
I noticed his new hairstyle immediately.
To evaluate how something stands out, the verb is often combined with adverbs such as 'positiv' (positively), 'negativ' (negatively), 'angenehm' (pleasantly), or 'unangenehm' (unpleasantly).
Seine laute Stimme fällt im Büro unangenehm auf.
His loud voice stands out unpleasantly in the office.
When you notice that a particular situation is the case, the structure 'Mir fällt auf, dass ...' (I notice that ...) is often used. What you notice is described in a subordinate clause with 'dass' (that).
Mir ist aufgefallen, dass du in letzter Zeit sehr müde wirkst.
I noticed that you have seemed very tired lately.
to notice / remember
Merken puts the person who perceives something at the center: someone merkt something. With auffallen, by contrast, the thing noticed is at the center, and the person is in the dative. Auffallen also often emphasizes that something attracts attention through a distinctive feature.

Mir fiel der Fehler in der Rechnung sofort auf.
The error in the invoice immediately stood out to me.
Ich merkte sofort den Fehler in der Rechnung.
I immediately noticed the error in the invoice.