
heftig
violent / intense
Of great strength, intensity, or force. Often refers to natural events, pain, or physical reactions.
Ein heftiges Gewitter zog in der Nacht über die Stadt.
A violent thunderstorm passed over the city during the night.
violent / intense
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violent / intense
Of great strength, intensity, or force. Often refers to natural events, pain, or physical reactions.
Ein heftiges Gewitter zog in der Nacht über die Stadt.
A violent thunderstorm passed over the city during the night.

heated / intense
Very intense and emotional in relation to arguments, feelings, or criticism.
Die beiden Politiker lieferten sich eine heftige Debatte im Parlament.
The two politicians had a heated debate in parliament.

insane / intense
A colloquial expression of surprise or admiration for something that is extreme, impressive, or shocking.
Wow, der neue Sportwagen von ihm ist echt heftig!
Wow, his new sports car is really insane!
'Heftig' can describe a noun (attributively) or define the manner of an action as an adverb. As an adverb, it remains unchanged in the sentence.
Es gab einen heftigen Streit.
There was a heated argument.
In its basic meaning, 'heftig' describes strong physical forces. It is often combined with natural events or physical reactions, e.g. 'heftiger Regen' (heavy rain), 'heftiger Schmerz' (severe pain), or 'heftiger Aufprall' (violent impact).
Nach dem Unfall hatte er heftige Kopfschmerzen.
After the accident, he had severe headaches.
When it comes to human interactions, 'heftig' describes emotional intensity. Typical combinations are 'heftige Kritik' (harsh criticism), 'eine heftige Diskussion' (a heated discussion), or 'heftige Gefühle' (intense feelings).
Die Entscheidung des Chefs löste heftige Reaktionen aus.
The boss's decision triggered strong reactions.
In colloquial speech, especially among young people, 'heftig' is used as an exclamation of surprise or admiration. It then means something like 'krass' (crazy/intense) or 'beeindruckend' (impressive).
Du hast die Prüfung mit 1,0 bestanden? Heftig!
You passed the exam with a 1.0? Insane!
strong
Stark and heftig can both describe very intense pain. Stark is the broader and more neutral term. Heftig often additionally emphasizes a particularly uncontrolled, forceful, or sudden onset.

Nach der Operation bekam sie plötzlich heftige Schmerzen.
She suddenly developed intense pain after the operation.
Nach der Operation hatte sie mehrere Stunden lang starke Schmerzen.
She had severe pain for several hours after the operation.