
notieren
to note
To briefly write something down so as not to forget it or in order to document it.
Bitte notieren Sie sich die Telefonnummer für den Rückruf.
Please note down the phone number for the callback.
to note / to be quoted
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to note
To briefly write something down so as not to forget it or in order to document it.
Bitte notieren Sie sich die Telefonnummer für den Rückruf.
Please note down the phone number for the callback.

to be quoted
(stock market language) To be traded on a stock exchange at a particular price or value.
Die Aktie des Technologieunternehmens notierte zum Handelsschluss fünf Prozent im Plus.
The technology company's stock was quoted five percent higher at the close of trading.
The verb 'notieren' (to note) belongs to the same word family as 'die Notiz' (note). Both words have the same root and refer to writing down information.
Ich mache mir immer Notizen, damit ich nichts Wichtiges vergesse.
I always take notes so that I don't forget anything important.
The meanings are easy to distinguish: when a person 'notiert' something, they write it down. When a stock or security 'notiert', its current stock market price is being stated.
Die Sekretärin notierte die wichtigsten Punkte der Besprechung.
The secretary noted the most important points of the meeting.
'Notieren' (to note) is very often used with a dative pronoun (mir, dir, sich). The construction 'sich (dative) etwas notieren' means that you write something down for yourself.
Kannst du dir bitte meine neue Adresse notieren?
Could you please note down my new address?
This meaning of 'notieren' (to be quoted) is technical language from finance and stock exchange contexts. In everyday life, the word is used almost exclusively to mean 'aufschreiben' (to write down).
Der DAX notierte am Mittag leicht im Minus.
The DAX was quoted slightly lower at midday.
to write
Both words mean putting something down in writing. Schreiben refers to the general activity, while notieren usually means making a brief note to remember something or use it later. Schreiben is suitable for a longer text; for a short, important piece of information, notieren is often more appropriate.

Ich notiere die Telefonnummer kurz in meinem Kalender.
I am quickly noting the phone number in my calendar.
Ich schreibe den Bericht heute Nachmittag am Computer.
I am writing the report on my computer this afternoon.