I have for some time wondered what the actual meaning of saṅkappa is. Here are some renderings used by the main translators:
thought, intention, aspiration, aim, resolve
What I have done was simply use the search function in the DPR to list occurences of the word throughout the Vinaya and the four Nikayas.
It seems that the word may sometimes be exactly equivalent to vitakka and sometimes has a connotation of wish, or desire, intention, purpose, aim, resolve... and I have come to the conclusion that a good rendering could be "[an] aspiration [that is articulated in words]". So here is how I have arrived to this conclusion:
First, cases when saṅkappa simply means vitakka, i.e. thought
The most blatant case is in the verses following AN 8.30, the Anuruddha-mahā-vitakka Sutta. Here I don't think anyone would disagree that the word vitakka is used in the entire sutta clearly meaning "thought". But the verses read:
Then there is AN 3.128 that compares unwholesome thoughts to flies:“mama saṅkappamaññāya,
satthā loke anuttaro.
“yathā me ahu saṅkappo,
tato uttari desayi.
Knowing my thoughts,
The Teacher, unexcelled in the cosmos,
Came to me through his power
In a body made of mind.
He taught in line with my thoughts,
And then further.
And then it refers to the same flies using the word saṅkappa:pāpakā akusalā vitakkā makkhikā
Evil, unwholesome thoughts are the ‘flies.’
Next, there is AN 4.35, where vitakka and saṅkappa are taken either as synonyms or as having very close meanings:Aguttaṃ cakkhusotasmiṃ,
One who is unguarded in the eye and ear,
Unrestrained in the sense faculties,
The flies will pursue,
[That is to say] thoughts based on lust.
In MN 60, either the words "thought" and "to think", or "to aspire" and "aspiration" could fit since "saṅkappa" is here an intermediary between views (diṭṭhi) and speech (vācā):So yaṃ vitakkaṃ ākaṅkhati vitakketuṃ taṃ vitakkaṃ vitakketi, yaṃ vitakkaṃ nākaṅkhati vitakketuṃ na taṃ vitakkaṃ vitakketi; yaṃ saṅkappaṃ ākaṅkhati saṅkappetuṃ taṃ saṅkappaṃ saṅkappeti, yaṃ saṅkappaṃ nākaṅkhati saṅkappetuṃ na taṃ saṅkappaṃ saṅkappeti. Iti cetovasippatto hoti vitakkapathe.
He thinks any thought he wants to think, and doesn't think any thought he doesn't want to think. He wills any resolve he wants to will, and doesn't will any resolve he doesn't want to will. He has attained mastery of the mind with regard to the pathways of thought.
An instructive expression is "sara-saṅkappā, memories and aspirations". It appears at MN 125:santaṃyeva kho pana paraṃ lokaṃ ‘natthi paro loko’ti saṅkappeti; svāssa hoti micchā**saṅkappo**.
Because there actually is the next world, when he is resolved that 'There is no next world,' that is his wrong resolve.
And again at SN 54.8:‘ehi tvaṃ, samma hatthidamaka, āraññakaṃ nāgaṃ damayāhi āraññakānañceva sīlānaṃ abhinimmadanāya āraññakānañceva sarasaṅkappānaṃ abhinimmadanāya āraññakānañceva darathakilamathapariḷāhānaṃ abhinimmadanāya
'Come you, good elephant tamer, tame the forest elephant by subduing his forest ways, by subduing his forest memories, and aspirations and by subduing his distress, his fretting and fever for the forest
More interesting yet is the expression "paripuṇṇa-saṅkappo, having fulfilled [his] aspiration", which makes it clear that "thought" would not really fit to render the meaning. At MN 29:bhikkhu cepi ākaṅkheyya: ‘ye me gehasitā sarasaṅkappā te pahīyeyyun’ti
If a monk should wish: 'May my memories & resolves related to the household life be abandoned
MN 146:so tena lābhasakkārasilokena attamano hoti paripuṇṇasaṅkappo.
He is gratified with that gain, honour, and renown, and his aspiration is fulfilled.
Then MN 78 hints that "saṅkappa" has something to do with language and thoughts articulated by concepts (which are crystallized as words):tā bhikkhuniyo nandakassa dhammadesanāya attamanā ceva paripuṇṇasaṅkappā ca
those bhikkhunı̄s are satisfied with Nandaka’s teaching of the Dhamma and their aspiration is fulfilled
The fact that a saṅkappa would be a wish or aspiration that is articulated with words could be corroborated by the stock definition of abyāpada, where the corresponding saṅkappa is formulated as a sentence (so made up of words). E.g. at AN 10.176:daharassa hi, thapati, kumārassa mandassa uttānaseyyakassa saṅkappotipi na hoti, kuto pana pāpakaṃ saṅkappaṃ saṅkappissati, aññatra vikūjitamattā!
Even the thought 'resolve' does not occur to [a stupid baby boy, lying on its back], so from where would it resolve on any evil resolve, aside from a little bad temper?
So in the end, the meaning that could fit all those contexts, it seems to me, would be an "aspiration that is articulated in words".abyāpannacitto hoti appaduṭṭhamanasaṅkappo: ‘ime sattā averā hontu abyāpajjā, anīghā sukhī attānaṃ pariharantū’ti.
He bears no ill will and is not corrupt in the resolves of his heart. [He thinks,] 'May these beings be free from animosity, free from oppression, free from trouble, and may they look after themselves with ease!'