die Notiz
note
A short written record used to remember something or to record information.
Ich habe mir eine Notiz gemacht, damit ich den Termin nicht vergesse.
I made myself a note so I don't forget the appointment.

note
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note
A short written record used to remember something or to record information.
Ich habe mir eine Notiz gemacht, damit ich den Termin nicht vergesse.
I made myself a note so I don't forget the appointment.

The noun 'die Notiz' (note) is closely related to the verb 'notieren' (to note/write down). When you write something down, you make a note.
Ich notiere mir schnell deine Telefonnummer.
I'll quickly note down your phone number.
To express that you write something down so you do not forget it, you use the fixed expression 'sich (Dativ) eine Notiz machen' (to make oneself a note).
Ich mache mir eine Notiz, damit ich daran denke, die Blumen zu gießen.
I'll make myself a note so I remember to water the flowers.
The meaning 'etwas bemerken' (to notice something) is used almost exclusively in the fixed expression 'von etwas/jemandem Notiz nehmen' (to take notice of something/someone). The preposition 'von' introduces a dative object here.
Niemand nahm von seinen neuen Schuhen Notiz.
No one took notice of his new shoes.
hint / notice
'der Hinweis' and 'die Notiz' can both be a short piece of information, often also in writing. The difference lies in the purpose: a 'Hinweis' is meant to help someone, draw attention to something, or give direction. A 'Notiz' is usually something you write for yourself or for another person so that you do not forget something. Learners may confuse the words when a short text is meant. As a practical rule: if the information is meant to help or warn, 'Hinweis' fits better. If it is about something written down to remember, 'Notiz' fits better.

Vor dem Telefonat macht sich Lena eine kurze Notiz.
Before the phone call, Lena makes a short note.
Am Eingang hängt ein Hinweis, dass die Tür ab 18 Uhr geschlossen ist.
There is a notice at the entrance saying that the door is closed from 6 p.m.