What really Sekha means?

Most of the dictionaries I found online, which mention that word, are Buddhist dictionaries: which give the definition which is specific to Buddhism.

I found one dictionary which defines the Sanskrit version of the word, which defines it as learning something slightly different from religion: i.e. learning the "science of pronunciation" when learning the vedas.

Definitions of śaikṣa

m. a young Brahman pupil studying with his preceptor, one who has recently begun to repeat the veda - View this entry on the original dictionary page scan.

mf(ī - )n. (fr. śikṣā - ) in accordance with right teaching or with rule, correct

शैक्षः [शिक्षां वेत्त्यधीते वा अण्] 1 A student who studies Śikṣā or the science of pronunciation, one who has just entered upon the study of the Vedas. -2 (Hence) A novice, tyro. -a. Well familiar with the studies or sciences; expert; Mb.6.97.28 (com. शैक्षं शस्त्रादिशिक्षा- संपन्नम्)

And

(from Śikṣā) in accordance with right teaching or with rule, correct

You might argue that's a "religious" learner too.

I guess that perhaps all education of that time (including science, mathematics, etc.) might have been connected with religion or taught by religious leaders, but I don't know.

The definition from the Pali Text Society says,

Sekha (& sekkha) [cp. Sk. śaikṣa; fr. siks, sikkhati] belonging to training, in want of training, imperfect Vin i.17, 248; iii.24; Dhs 1016; one who has still to learn, denotes one who has not yet attained Arahantship D

Also the The Sikh Encyclopedia says,

SIKH. The word sikh goes back to Sanskrit sisya, meaning a learner or disciple. In Pali, sisya became sissa. The Pali word sekha (also sekkha) means a pupil or one under training in a religious doctrine (sikkha, siksa).

According to my dictionaries,

• sekha means student, beginner, aspirant
• sikkhā (as in sikkhāpada of the five precepts) means training, instruction, education -- including both the learning and the teaching sides

In general, sekha/sekkha seems to mean someone who is still striving, still looking up to a higher level of mastery. The meaning seems to be broad and not confined to the religious domain.

In Saṅgītisutta three types of persons in the world are mentioned: sekkha (learner), asekkha (adept) and nevasekkha nāsekkha (ordinary person or puthujjana)

Tayo puggalā—sekkho puggalo, asekkho puggalo, nevasekkho nāsekkho puggalo
Saṅgītisutta
Three kinds of persons, to wit, the learner, the adept, he who is neither.
Saṅgītisutta [en]

A sekha is someone who trains himself in higher virtues, training the mind to a higher degree and training for higher wisdom or basically someone who's training himself in the eightfold path. There are 7 types of sekhas (1) the path to stream-entry; (2) the fruition of stream-entry; (3) the path to once-returning; (4) the fruition of once-returning; (5) the path to non-returning; (6) the fruition of non-returning; (7) the path to arahantship

Sekho, sekho’ti, bhante, vuccati. Kittāvatā nu kho, bhante, sekho hotī”ti? “Sikkhatīti kho, bhikkhu, tasmā sekhoti vuccati.
Kiñca sikkhati? Adhisīlampi sikkhati, adhicittampi sikkhati, adhipaññampi sikkhati. Sikkhatīti kho, bhikkhu, tasmā sekhoti vuccatīti.
Sekkhasutta

Venerable sir, it is said a trainee. How is one a trainee? Bhikkhu, one trains, therefore he is called a trainee.
In what does he train? He trains in higher virtues, training the mind to a higher degree and training for higher wisdom.
Sekkhasutta [en]

An asekha is someone who's gone beyond the training or basically an arahant.

Asekho asekho’ti, bhante, vuccati. Kittāvatā bhante, bhikkhu asekho hotī”ti? “Idha, bhikkhu, bhikkhu asekhāya sammādiṭṭhiyā samannāgato hoti, asekhena sam­māsaṅkap­pena samannāgato hoti, ... Evaṃ kho, bhikkhu, bhikkhu asekho hotī”ti
Paṭha­ma­a­sekha­sutta

Venerable sir, it is said, `gone beyond the training' How is the bhikkhu gone beyond the training? Here, bhikkhus, the bhikkhu is endowed with perfect right view, perfect right thoughts, perfect right speech, perfect right activity, perfect right livelihood, perfect right endeavour, perfect right mindfulness, perfect right concentration perfect right knowledge and perfect right release gone beyond the training. Such a one is gone beyond the training.
Paṭha­ma­a­sekha­sutta [en]