What is the etymology of "byāpā­da­" The standard description of Wrong Thought (micchāsaṅkappo) in Pali is 


  Katamo ca, bhikkhave, micchāsaṅkappo? Kāmasaṅkappo, ­byāpā­da­saṅkappo, vihiṃ­sāsaṅ­kappo—ayaṃ, bhikkhave, micchāsaṅkappo. (from MN 117)


The translation says:


  “And what, bhikkhus, is wrong intention? The intention of sensual desire, the intention of ill will, and the intention of cruelty: this is wrong intention.


I have problems understanding the difference between byāpā­da­ (~ ill will) and vihiṃ­sā (~ cruelty). I know that vihiṃ­sā means something like "wishing someone harm". But I didn't find where the word byāpā­da­ comes from and in what quality the meaning of it is different from vihiṃ­sā. Can someone please help me out?
To help understand the differences between the two words, let’s try to understand the meaning of the words independently.  Vyäpäda is ill will. It is a stronger word than patigha. Because of kamachanda, “dosa” or long-lasting hateful situations arise. In the present day Sinhala language, we say ‘dvesa’ for the term ‘dosa’. This long-lasting hateful situation, at its extreme brings out the second of the five hindrances, ‘Vyäpäda’. We can break this word into “vaya”+”pada”. “Vaya” means decline even in native Sinhala. and “Pada” means walk towards.  Thus ‘Vyäpäda’ means one is on a path of (moral) decline. kamachanda and Vyäpäda are the main reasons that we suffer. By disciplining ourselves through speech and bodily actions we can remove any thoughts of extreme greed and hate as they come to the mind.

Vihimsa can be said as cruelty and harmfulness. Its opposite is harmlessness (avihimsa). The following Pali phrase in short means MOLEST NONE…. It’s full meaning is… “He who seeks his own happiness by harming others who also desire to have happiness will not find happiness hereafter. 


  ”Sukha kamani bhutani yo dandena VIHIMSATI
  Attano sukham esano pecca so na labhate sukham. 


If we take ‘Sankappo’ to mean thoughts, then…     Nekkhamma-sankappo  is  ‘thoughts of renunciation’, i.e., thoughts to cultivate when being at ease in quiet, solitary places. 

Avyäpäda -sankappo  is ‘thoughts of non-anger, non-hatred’: We don’t have to keep 
thinking about our own bad points or the bad points of others and let these thoughts of ill-will fester. 

Avihinsa-saakappo is ‘thoughts of not doing harm’, not creating trouble or doing harm to ourselves and others. i.e., This also entails not thinking about our own shortcomings, which would depress us; if we think about our own shortcomings, it’ll spread to that of others shortcomings too. For this reason, the wise would lift their thoughts to the level of goodness so that they project love and good will for themselves, and in turn feel love and good will for others too.