This word describes deceiving, defrauding or misleading someone on purpose (the noun Betrug (m.) means “fraud”). The context can also be cheating in a relationship.
It is the most serious of the words featured here
Example:
Die Firma hat die Verbraucher betrogen. The company has cheated the consumers.
Schummeln / Mogeln
These somewhat less serious words are used to describe dishonest actions when playing games, or when cheating on tests (the word for copying someone else’s work is abschreiben or spicken, and a “cheat sheet” is called Spickzettel (m.))
Example:
Ich spiele nicht mit ihm weil er immer schummelt. I’m not playing with him because he always cheats.
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Fremdgehen
This word describes the action of being unfaithful (or “having a bit on the side”) in a relationship. It literally translates to “going strange”.
Example:
Er ist mit ihr fremdgegangen. He cheated (on someone) with her.
Schwindeln
This word is familiar, it means “to swindle”. Originally it described giddy people and is related to the German schwindelig, meaning “dizzy”.