kämmen
to comb
To arrange and smooth hair with a comb. Often used reflexively ('sich kämmen') when arranging one's own hair.
Bevor wir gehen, muss ich mir noch schnell die Haare kämmen.
Before we go, I still need to quickly comb my hair.

to comb / search
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to comb
To arrange and smooth hair with a comb. Often used reflexively ('sich kämmen') when arranging one's own hair.
Bevor wir gehen, muss ich mir noch schnell die Haare kämmen.
Before we go, I still need to quickly comb my hair.

The verb 'kämmen' (to comb) derives directly from the noun 'der Kamm' (the comb). The action therefore describes the use of a comb.
Ich habe meinen Kamm verloren und kann mich nicht kämmen.
I lost my comb and can't comb my hair.
When arranging one's own hair, 'kämmen' (to comb) is often used reflexively with a dative pronoun. The structure is: 'sich (dative) die Haare (accusative) kämmen' — literally, 'to comb oneself the hair'.
Kannst du mir bitte die Haare kämmen?
Can you please comb my hair?
In the meaning 'durchsuchen' (to search), the word is used figuratively. You imagine an area being searched as systematically and completely as a comb moves through hair.
Die Rettungskräfte kämmen das gesamte Gebiet nach Überlebenden.
The rescue workers are searching the entire area for survivors.
When 'kämmen' (to comb/search) is used in the context of police, searches, or investigations, it almost always means 'systematisch durchsuchen' (to search systematically). The object is then a place such as a forest, a house, or a site.
Die Polizei hat das verlassene Gebäude komplett gekämmt.
The police searched the abandoned building completely.
The meaning related to textile fibers is purely technical language. You only find it in texts about the production of yarns and fabrics.
In der Fabrik wird die Baumwolle maschinell gekämmt.
In the factory, the cotton is combed by machine.
to search
'durchsuchen' and 'kämmen' can both mean that an area is searched very thoroughly. 'durchsuchen' is the more general word and works for rooms, bags, houses, or other things as well. 'kämmen' in this meaning is used more for a larger area, for example a forest, a field, or a neighborhood. It sounds figurative: you move through the area very systematically, almost like a comb through hair. In everyday language, 'durchsuchen' is usually more neutral and more often appropriate. 'kämmen' feels stronger and is often used for police, rescue, or search operations.

Die Helfer kämmen den Wald nach dem vermissten Kind.
The volunteers are combing the forest for the missing child.
Sie hat ihre Tasche durchsucht, weil der Ausweis nicht mehr da war.
She searched her bag because her ID was missing.