The name "Vael" meant in the old days "Wise woman" because the profession of a Vael was only taken by women or their daughters, granddaughters, mothers, sisters... you name it. Technically it could be also taken by men, but most of them deemed it to be "unworthy" or "womens work". Until they got healed/cured. Some of those men started to work as the assistant or the apprentice of a Vael until becoming one. Which also meant that the name "wise woman" was getting pretty outdated, so it changed to "wise being". Especially when not only humans were allowed to be a Vael.
One major problem with a women-only profession: not enough wise women or wise men. Wise beings in general. Even when the procreate, they couldn't compete against the masses of beings and the decay of life, so the profession of the Vael was endangered. War, pestilence, famine and mostly loneliness were also a thing.
Vael is a profession originated long before even the Dragon Sun Empire or the Dragonborn were created.
Originally a human-only profession, over the years the human Vaels allowed other beings into their profession. Some of them like the Wood Elves were born to do this because of their relationship to nature and the Eternal Life. Dwarves for example are rare because they have an affinity for metal, stone and earth and not so much for nature as in wood and plants, but there are exceptions. Even some of the feared Garladan were invited into the Nox Vael and into the profession because they took an oath. What kind of oath? That is a thing between the tribunal members and the Garladans.
The only difference between a witch/sorcerer and a Vael is the source of their power.
The difference in power from a witch or a sorceres is that Vael have druidic powers. For the unknowing or ignorant person it might look and feel like magic - which it is basically - but while witches and sorceresses draw their power from beyond the veil, the Vael use the power within earth & tree, the power of nature; the power of the Eternal Life.
The next great difference between the two power sources is their way of healing. While non-Vaels draw powers from beyond the veil and execute spells, rituals, healings in the blink of an eye, the Vael magic operates much slower. One of the reasons the Nox Vael has a duration of many days. But the reason behind that is: nature has all time in the world. Healing a child might be an emergency, but you can't rush the powers of nature. So everything might take a bit (or a lot) of time.
During the first days of the Vael they needed to study things all on their own or with the help of other women. Which was mostly a lot of learning by doing - and some by dying - but eventually the profession came into play and teachers with apprentices (be it taken in or the own daughters) roamed the continent.
The training is not as hard as one would imagine. It is a lot of responsibility because you always tend to living beings, be it the plant in your backyard or the ill rabbit or the pregnant woman who is about to give birth and might lose the child. If you do your profession the wrong way, something or someone dies.
The training might be not as hard as one might imagine, but it is thorough and most apprentices don't get to wear the title of Vael before their twentieth summer.
Only the tribunal will grant you the title of Vael if you surpass their test of knowledge and practice.
Before the Nox Vael the spread of knowledge was slow and stagnated for a long time. Only by chance certain tricks, practices or tipps were given from one Vael to another. Some older Vaels sent their apprentices into the world so they can visit other Vaels and settle down if they do not wanted to inherit their mothers/teachers place.
With the Nox Vael it was a bit easier. Elves tend to do things a bit different than a dwarf or a Garladan. The chatting between the rituals was helpful and because Vaels cover a particular area in their vicinity the knowledge spread faster in all corners of Koria. Not that every Vael knows everything. But some things were known while others stayed hidden.