Buddhist Brahmachariya, Brahmin Brahmachariya, celibacy, chastity Here is my main question #1
What is the difference between sutta defn. of Brahmacariya and 1) brahmin Brahmacariya predating Buddhism and 2) celibacy and chastity?
defn.: celibacy
the state of abstaining from marriage and sexual relations.
What is the difference between celibacy and abstinence? Although many people use “celibacy” and “abstinence” interchangeably, there is a difference between the two terms. Abstinence usually refers to the decision not to have penetrative sex. ... Celibacy is a vow to remain abstinent over an extended period of time.
defn.: chastity
the state or practice of refraining from extramarital, or especially from all, sexual intercourse.
What is an example of chastity? The definition of chastity is a quality held by someone pure, modest or celibate. A virgin is an example of chastity. Faithful married couples are examples of chastity. ... The boy's friends laughed at him when he took a chastity pledge and promised to not have sex.
Note that ‘brahmacariya’ goes much farther than ordinary defn. of ‘chastity’ and ‘celibacy’
Here is my main question #2
Not even having a thought of lust is the EBT definition of brahmacariya, avoiding sex and any kind of physical or mental sexual activity. Ordinary defintions of ‘celibacy’ and ‘chastity’ tend to use physical activity to determine status. EBT buddhism focuses on the mental causes that can preempt physical manifestations of lust, kāma ‍. (sutta refs?)
I think there's a sutta (or two) in AN that answers both questions, where the Buddha criticizes Brahmans of his time not living up to brahmacariya.
PED definition:
: Brahmacariya (neuter) [brahma + cariya] a term (not in the strictly Buddhist sense) for observance of vows of holiness, particularly of chastity: good and moral living (brahmaṃ cariyaṃ brahmāṇaṃ vā cariyaṃ = brahmacariyaṃ Pj I 151); especially in Buddhist sense the moral life, holy life, religious life, as way to end suffering, Vin I 12, 19, renouncing the world, study of the Dhamma D I 84, 155; II 106; III 122f., 211; M I 77, 147, 193, 205, 426, 463, 492, 514; II 38; III 36, 116; S I 38, 43, 87, 105, 154, 209; II 24, 29, 120, 219, 278, 284 (°pariyosāna); III 83, 189; IV 51, 104, 110, 126, 136f., 163, 253, V 7f., 15f., 26f., 54f., 233, 262, 272, 352; A I 50, 168, 225; II 26, 44, 185; III 250, 346; IV 311; V 18, 71, 136; Snp 267, 274 (vas-uttama), 566, 655, 1128; Thag 1027, 1079; It 28, 48, 78, 111; Dhp 155, 156, 312; Ja III 396; IV 52; Pv II 913; Dhp-a IV 42 (vasuttamaṃ); Vibh-a 504. — brahmacariyaṃ vussati to live the religious life A I 115 (cf. °ṃ vusitaṃ in formula under Arahant II A); °assa kevalin wholly given up to a good life A I 162; °ṃ santānetuṃ to continue the good life A III 90; Dhp-a I 119; komāra° the religious training of a well-bred youth A III 224; Snp 289.
— abrahmacariya unchastity, an immoral life, sinful living M I 514; D I 4; Snp 396; Pj I 26;
'abrahmacariyā' = no sex, no masturbation, per Vinaya
for a sutta explanation, MN 117 says:

And what is right action that is accompanied by defilements, has the
attributes of good deeds, and ripens in attachment?
Katamo ca, bhikkhave, sammākammanto sāsavo puññabhāgiyo upadhivepakko?
Refraining from killing living creatures, stealing, and sexual
misconduct.
Pāṇātipātā veramaṇī, adinnādānā veramaṇī, kāmesumicchācārā veramaṇī—
And what is right action that is noble, undefiled, transcendent, a
factor of the path?
Katamo ca, bhikkhave, sammākammanto ariyo anāsavo lokuttaro maggaṅgo?
It’s the desisting, abstaining, abstinence and refraining from the
three kinds of bad bodily conduct in one of noble mind and undefiled
mind, who possesses the noble path and develops the noble path.
Yā kho, bhikkhave, ariyacittassa anāsavacittassa ariyamaggasamaṅgino
ariyamaggaṃ bhāvayato tīhi kāyaduccaritehi ārati virati paṭivirati
veramaṇī—
MN 117

the three kinds of bad bodily conduct includes any type of bodily conduct that maintains or increases the hindrance of sensual desire, as follows:

And what is the fuel for the five hindrances?
Ko cāhāro pañcannaṃ nīvaraṇānaṃ?
You should say: ‘The three kinds of misconduct.’
‘Tīṇi duccaritānī’tissa vacanīyaṃ.
AN 10.61

sexual thoughts are not included in 'brahmacariyā' because only 'abrahmacariyā' or 'kāyaduccaritehi' are included in the Right Action factor of the Noble Eightfold Path

And what is right action?
Katamo ca, bhikkhave, sammākammanto?
Avoiding killing living creatures, stealing and sexual activity.
Yā kho, bhikkhave, pāṇātipātā veramaṇī, adinnādānā veramaṇī,
abrahmacariyā veramaṇī—
This is called right action.
ayaṃ vuccati, bhikkhave, sammākammanto.
SN 45.8

sexual thoughts are obviously 'wrong thought' but not 'wrong action', as follows;

And what is wrong resolve? Being resolved on sensuality, on ill will,
on harmfulness. This is wrong resolve.
MN 117

as for Brahmins &amp; sex, the sutta sought is possibly AN 5.192, even though such a sutta is not for Buddhists. This sutta appears to say a brahmin is equal to Brahmā when they go forth from the lay life to homelessness and master the Four Brahma Vihara. If the 4th Brahma Vihara of equanimity is mastered then obviously any type of sexual activity is excluded.