Translationg the terms makes a semantic rendering important. The English resourse translates क्रोध [krodha] as 'anger' wrath, passion, etc.' with the same definition for कोप​ [kopa] plus defining it as 'morbid irritation or disorder of the humors of the body'. The compound noun कोपकारण [kopakāraṇa] is rendered there as 'cause of anger', by which I deduce that in English translation these two words are mainly synonymous and covered by a same semantic field.

Tibetan language renders both क्रोध [krodha] and कोप​ [kopa] as ཁྲོ་བ་ [khro ba] and ཁྲོས་པ་ [khros pa] respectively.

The German resourse covers both terms with the word 'wrath' with क्रोध [krodha] being in some context synonymous to 'passion'. Ah, and कोप​ [kopa], too.

So my question is, are there any other possible distinction between the meaning of these two words except of possible [structured] क्रोध [krodha] VS [non-structured] कोप​ [kopa]?

Are these two words cognates?

कोप and क्रोध are not cognates (or more accurate, doublets, since they are in the same language). They have different Sanskrit roots (कुप् and क्रुध्) and no proposed common source in Proto-Indo-European.

They at least have a large semantic overlap even if they aren't exactly the same. क्रोध is not uncommon in Hindi as a Sanskrit borrowing (Sanskrit is a superstrate of Hindi), while कोप is rare.

( Since I am not an expert on Tibetan and German, this answer might be biased to Sanskrit and Hindi but this won't affect the answer asked for )

I have generally seen krodha when there is a negative connotation of anger or when the anger might result in a (mythological) curse and kopa when it's godly/well-reasoned/non-cursing anger. AFAIK cognates are a pair of words which are similar semantically and phonetically but are from 2 different languages, but krodha and kopa are both used simultaneously (at least now) in Sanskrit and Hindi.

P.S. Now though, in Hindi, generally, kopa is used to refer it's religious nature and krodha is used in almost every sense.

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