
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.

to take notice of
To notice, pay attention to, or acknowledge something. Often used in the negative form to express disinterest.
Er ging an mir vorbei, ohne von mir Notiz zu nehmen.
He walked past me without taking notice of me.
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.
message / news
A Nachricht is sent to someone, while a Notiz primarily records information in writing. If you want to inform another person, you write a Nachricht; if you want to remind yourself of something, you make a Notiz.

Ich schreibe mir eine Notiz mit der neuen Uhrzeit.
I'm writing myself a note with the new time.
Ich schicke Tom eine Nachricht mit der neuen Uhrzeit.
I'm sending Tom a message with the new time.