der Kleber
glue
A substance used to join or stick two or more objects together; an adhesive.
Ich brauche einen starken Kleber, um die zerbrochene Tasse zu reparieren.
I need a strong glue to repair the broken cup.

glue / sticker
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glue
A substance used to join or stick two or more objects together; an adhesive.
Ich brauche einen starken Kleber, um die zerbrochene Tasse zu reparieren.
I need a strong glue to repair the broken cup.

'Der Kleber' (glue/sticker) is derived directly from the verb 'kleben' (to stick). The ending '-er' here refers to the means or tool with which the action is carried out — that is, the thing that sticks.
Mit diesem Kleber kannst du fast alles kleben.
You can glue almost anything with this glue.
When referring to adhesive, 'Kleber' (glue) is often combined with adjectives such as 'stark' (strong), 'flüssig' (liquid), or 'schnelltrocknend' (quick-drying). People also often talk about a 'Tube Kleber' (tube of glue).
Für diese Reparatur brauchst du einen wirklich starken Kleber.
For this repair, you need a really strong glue.
You can tell from the context whether glue or a sticker is meant. If the text mentions 'sammeln' (to collect), 'verzieren' (to decorate), or 'bunte Kleber' (colorful stickers, in the plural), it usually means stickers.
Mein kleiner Bruder sammelt Kleber von verschiedenen Fußballvereinen.
My little brother collects stickers from different football clubs.
Using 'Kleber' to mean a sticker is mainly colloquial. In more formal contexts or in written German, this meaning is used less often.
Sein Laptop ist voller bunter Kleber.
His laptop is full of colorful stickers.
sticker
'der Aufkleber' and 'der Kleber' can both mean a small object that you stick onto something in colloquial language. In this sense, 'Kleber' is an informal term for 'Aufkleber' (sticker). But there is an important risk of confusion: 'Kleber' very often also means the substance used to glue things together. So 'Aufkleber' is more precise when you mean the picture or label with an adhesive back. When the topic is crafts or repairs, 'Kleber' usually means glue.

Emma sucht den Kleber, weil sie das Papier reparieren will.
Emma is looking for the glue because she wants to repair the paper.
Wir brauchen einen Aufkleber, damit jeder sein Heft erkennt.
We need a sticker so everyone can recognize their notebook.