Buddhist Brahmachariya, Brahmin Brahmachariya, celibacy, chastity
'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.