to stamp / label
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to stamp
To press a stamp onto something in order to cancel, validate, or mark it, for example a postage stamp or a ticket.
Bitte vergessen Sie nicht, Ihre Fahrkarte vor Fahrtantritt abzustempeln.
Please don't forget to stamp your ticket before starting your journey.
'Abstempeln' (to stamp / label) is a separable verb. In a main clause, the prefix 'ab-' comes at the end of the sentence. In subordinate clauses or in the infinitive, the verb stays together.
Der Kontrolleur stempelt die Fahrkarten ab.
The inspector stamps the tickets.
You can recognize the meaning from the object: if it is about concrete things like 'Fahrkarte' (ticket) or 'Briefmarke' (postage stamp), the literal meaning is intended. If the object is a person and the preposition 'als' follows, it is the figurative, negative judgment.
Du musst den Brief noch abstempeln, bevor du ihn einwirfst.
You still have to stamp the letter before you drop it in the mailbox.
In the figurative meaning, 'abstempeln' (to label) is almost always used with the preposition 'als'. The structure is: 'jemanden / etwas als ... abstempeln' (to label someone / something as ...).
Seine Idee wurde sofort als unrealistisch abgestempelt.
His idea was immediately labeled as unrealistic.
to mark / characterize
'kennzeichnen' and 'abstempeln' can both express that something receives a visible mark. But 'kennzeichnen' is broader: the mark can be a label, a color, a symbol, or another kind of marking. 'abstempeln' is more specific and means that a stamp is pressed onto something, for example onto a ticket or a form. If a stamp is really being used, 'abstempeln' is more natural. If you simply mean a marking in general, 'kennzeichnen' fits better.
Vor der Fahrt muss Lena ihre Fahrkarte abstempeln.
Before the trip, Lena has to stamp her ticket.
Die Kisten für den Umzug sind mit farbigen Aufklebern gekennzeichnet.
The boxes for the move are marked with colored stickers.