dampfen
to steam
To give off steam or vapor that forms when a liquid, usually water, is heated.
Der heiße Tee dampfte in der Tasse.
The hot tea was steaming in the cup.

to steam / to vape
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to steam
To give off steam or vapor that forms when a liquid, usually water, is heated.
Der heiße Tee dampfte in der Tasse.
The hot tea was steaming in the cup.

The verb 'dampfen' (to steam) is derived directly from the noun 'der Dampf' (steam). It describes the action of giving off steam or treating something with steam.
Im Winter dampft der Atem in der kalten Luft.
In winter, your breath steams in the cold air.
In the meaning 'to cook food', 'dampfen' (to steam) is used with an accusative object. In the other meanings, the verb usually stands without an object to describe a state.
Ich dampfe den Brokkoli nur kurz, damit er knackig bleibt.
I steam the broccoli only briefly so that it stays crisp.
The use of 'dampfen' (to vape) for smoking an e-cigarette is a modern, colloquial meaning. In formal contexts, you would be more likely to paraphrase it.
Immer mehr junge Leute dampfen statt zu rauchen.
More and more young people vape instead of smoking.
When someone is very angry, the colloquial expression 'vor Wut dampfen' (to fume with anger) is used. Here the verb is used in a figurative sense.
Als er die Rechnung sah, hat er innerlich vor Wut gedampft.
When he saw the bill, he was inwardly fuming with anger.
to cook / to boil
'kochen' and 'dampfen' both have to do with heat and can occur in the kitchen. You use 'kochen' when you prepare food by heating it, or when water boils. 'dampfen' usually means that steam rises, for example from hot food or water. For cooking, 'dampfen' is more precise when food is not sitting in water but is cooked by hot steam. The words can be confused because cooking often produces steam. In practical terms: water 'kocht', soup 'kocht', but hot tea 'dampft'. Both words can also figuratively express strong anger, but 'kochen vor Wut' (to boil with rage) is the more common fixed expression.

Nach dem Spaziergang dampft der heiße Tee auf dem Küchentisch.
After the walk, the hot tea is steaming on the kitchen table.
Heute koche ich eine Suppe, weil draußen so schlechtes Wetter ist.
Today I'm cooking soup because the weather outside is so bad.