vāyāma vs virya?

I think of samma-vāyāma (right effort) as following after samma-saṅkappa (right intention or resolve) -- i.e. it's one thing to intend something, another thing to make the corresponding effort.

I think that viriya describes the quality of an effort -- e.g. is it a strong effort, or is it a feeble and ineffective effort?

Wikipedia's Indriya confirms the literal or etymological connection with Indra, but says that in Buddhism it refers to faculties including the six senses. One of the "right efforts" is indriya-samvara i.e. "guarding the sense-doors".

samma padhana (right exertion from 37 bodhi pakkhiya), viriya-indriya, viriya sambojjhanga (of 7 awakening factors), samma vayamo (right effort of noble eightfold path) are equivalent. The slightly different official definition for each term, is meant to highlight a particular aspect of right effort.

You'll notice in the right effort definition (SN 45.8), all of those words are found in the formula (vayamati/vayamo, viriya, padahati/padhana).

Another word that frequently occurs in the suttas, such as in the satipatthana formula, 'ātāpi' (ardency), is a code word that also means the same right effort formula (see AN 4.14 verse at end) http://lucid24.org/an/an04/an04-0014/index.html

Their contextual use in the suttas is the same, as follows:

And what is right effort? Katamo ca, bhikkhave, sammāvāyāmo?

It’s when a mendicant generates enthusiasm, tries, makes an effort, exerts the mind, and strives so that bad, unskillful qualities don’t arise. Idha, bhikkhave, bhikkhu anuppannānaṃ pāpakānaṃ akusalānaṃ dhammānaṃ anuppādāya chandaṃ janeti vāyamati vīriyaṃ ārabhati cittaṃ paggaṇhāti padahati,

SN 45.8

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And what is the faculty of energy? Katamañca, bhikkhave, vīriyindriyaṃ?

It’s when a mendicant lives with energy roused up for giving up unskillful qualities and embracing skillful qualities. They’re strong, staunchly vigorous, not slacking off when it comes to developing skillful qualities. Idha, bhikkhave, ariyasāvako āraddhavīriyo viharati akusalānaṃ dhammānaṃ pahānāya, kusalānaṃ dhammānaṃ upasampadāya, thāmavā daḷhaparakkamo anikkhittadhuro kusalesu dhammesu.

They generate enthusiasm, try, make an effort, exert the mind, and strive so that bad, unskillful qualities don’t arise. So anuppannānaṃ pāpakānaṃ akusalānaṃ dhammānaṃ anuppādāya chandaṃ janeti vāyamati vīriyaṃ ārabhati cittaṃ paggaṇhāti padahati

SN 48.10

The word 'vāyāma' is derived from 'vi + ā + yam' where 'yam' or 'yāma' appears to mean 'restraint', 'don't do', 'reining in' or 'control'. One fluent in Pali will need to explain how 'vi + ā' modify 'yāma'.

The word 'viriya' I guess is derived from 'vīra + ya' and is said to literally mean 'state of a strong man'. 'Vīra' means 'strong', 'brave' or 'heroic' thus 'ya' must mean 'state'.

Therefore, merely guessing, 'viriya' appears to be a 'thing', namely, 'energy'; where as 'vāyāma' appears related to acting or related to a verb, i.e., possibly a 'verbal noun'. In other words, in the Pali above, there is the phrase 'vāyamati vīriyaṃ'. Here, 'vāyamati' (due to ending in 'ati') is a verb; where as 'vīriyaṃ' is a noun. Thus, the phrase 'vāyamati vīriyaṃ' appears to mean: 'to exercise energy' or 'to exert energy'.

In summary, 'vayama' appears related to the action of acting; where as 'viriya' appears related to the quality of acting. This said, I could be wrong, here, because I am merely guessing.

Sometimes a look at opposite terms can help.

For avāyāmaṃ we have weakly directed effort:

SN11.1:3.3: without working for it or trying hard—

For avīriyā we have apathetic lethargy:

MN60:21.7: All sentient beings, all living creatures, all beings, all souls lack control, power, and energy. Molded by destiny, circumstance, and nature, they experience pleasure and pain in the six classes of rebirth.’