Polish husarz (hussar) (also known under Old Polish word usarz) is originally Hungarian. Literally - some Hungarians who fought Turks emigrated to Poland in middle 1400s. So 15th century Polish hussars would be actual Hungarians initially or after few decades Poles armed and organized like the originals. Which meant light cavalry, which would operate alongside heavier lancer units at the time.
However, the hussars quickly gained in prominence, and by the beginning of the 1500 they were the backbone of Polish cavalry. In fact, they were already used for deciding charges in battle, with most prominent example of such being The Battle of Orsza in 1514.
As a side note on latest research on the origins - P. Grotowski speculates that hussars can trace their origins to Byzantium's light cavalry from 10th or 11th century.
Konstanty Górski, Historya Jazdy Polskiej and
Piotr Grotowski, Trapezici, tasinarci i husarze – z rozważań nad genezą husarii
However, by the end of 16th century Polish husarze were employed in the role of the shock cavalry (for example Battle of Lubiszewo [or Lubieszów] in 1577), following the reforms of newly elected king Stefan Batory (coronated in 1576).
[In registry documents, husarskie units were marked with abbreviation p.t.d.p. - (p)ancerz (armor), (t)arcza (shield), (d)rzewo (lance), (p)rzyłbica (bascinet). The sabre was not mentioned because it was expected for everyone to have one. Z dziejów husarii - Radosław Sikora
While at this time 80% of Polish cavalry force was of "rackiej organizacji" (that is: Hungarian hussars style), Batory created essentially new force. On one hand, he divided existing units by the nationality and mandated regulation armament of the both Polish and Hungarian hussars, of which most important change was requiring use of light armor. On the other hand there was the formation of completely new force, which required even more and better equipment from the volunteers
According to surviving documents, Batory required from anyone who wanted to join his "husarskie chorągwie koronne" to have: iron armor, gauntlets and helmet, wooden lance (which was of unique polish design and manufacture), sabre and pistols. Documents also mentioned fearthers and other ornaments, both for splendor and to demoralize the enemy - from which evolved characteristic wings of later years.
Point of note: name "husarskie chorągwie koronne" (crown hussars units) did not mean they were "royal own" - it denoted the actual, elite, winged hussars, of which at least some were formed privately by dukes and princes, too. And, of course, this would be the easy to determine point when polish hussar units became usarze, and actual hussar units became rackie, then later kozackie and finally lisowczyki. Though, as mentioned earlier, the divergence in actual employment in battle between hussars in Poland and hussars elsewhere happened earlier - Battle of Orsza was the first known instance where hussars were used to break through enemy forces, which is obviously not the proper use of light cavalry.
This designation may cause additional confusion for non-polish speakers, because Res Publica Poloniae at that time comprised of Old Polish Kingdom ("Korona" - eng. Crown) and Great Duchy of Lithuania ("Litwa"), and later also Ukraina, as Republic of Poland was actually an union of two (Poland and Lithuania) and later three (Poland, Lithuania and Ukraine) nations, each with their own nominal head, subordinated to Polish King only. Thus if there was a need of concentrating large army from all regions, they will be divided into "national" corps, designated Koronne, Litewskie i Ukraińskie armiesx, after geographical region. Yet all three would have husarskie chorągwie koronne in their order of battle, and substantial part would be, as mentioned, raised by private parties (at the time they would be called magnates).
Sorry (not) for eventual confusion.
Husaria - Jerzy Cichowski, Andrzej Szulczyński as well as
Description de l'Vkranie depvis les confins de la Moscovie jvsqu'avx limites de la Transylvanie - Guillaume Levasseur de Beauplan
Of course the Batory reforms weren't instantaneous, but starting with 1577 and with Muscovite campaigns of 1579-81, Polish Hussars were known to be almost exclusively shock cavalry of their true fame.
There has to be a point made here: technically Polish husarze weren't heavy cavalry - those were different unit type called "pancerne" - they were used mostly (though not exclusively) as a force to achieve breakthrough by concentrated charge on weakest point of enemy's force. Those breakthroughs were then exploited by attacks of "choragwie pancerne i kozackie" - units of heavy and light cossack (not: Cossack) cavalry.
Polish heavy cavalry would be an chainmail, iron helmet and shield armored, sabre, spear and bow-and-arrow armed unit, while cossacks (or "lisowczyk" - this name became norm later, to distinguish from actual, ethinic Cossacks) were light, ususally un-armored units.
Most importantly, Polish husarze were definitely an universal soldiers - they were best at breakthrough charge, but would be excellent in pursuit, very good at escort and would do very well as an infantry, too. They had their use even in fortified defense - to break up infantry charging the walls with powerful sallies. They were truly elite units, comprising often no more than 10% of the total numbers. This could be done because they were able to charge multiple times during each battle (historical sources mention that 2-3 were nothing unusual, with at least one encounter seeing 10 charges).
By now it should be obvious that not everybody could be an usarz. Because it required substantial expenditure to afford the equipment (of which most expensive were war horses, specially raised and trained, and which usarz needed several), it was almost exclusively noble-born profession. How they became such a force is well explored, and a very easy to understand movie, describing who were the people joining the hussars can be found, too: Born For The Saber.
It is no mystery, as well, why it was never a large force, at the peak being just over 8000 strong nationally, especially in a country that would be largest in Europe at the time.
But back to designations, types and use of units. While technically correct, designation of Polish husaria as "heavy" is not precise: they would place above cuirassiers in terms of armor and arms, with actual heavy (pancerne) units below cuirassiers in same terms.
Successful husarz charge required follow-on attack of both pancerne and lisowczyk units to decide the battle, due to mostly low numbers of hussars.
Undoubtedly there were still Hungarian units in Polish forces that were calling themselves hussars, but being light (or light-ish) cavalry, they were started to be called "rackie", to distinguish the two, now very dissimilar, unit types, as mentioned earlier.
"Jazda Racka", which is the general name for troops arriving from Hungary to Poland comes from Old Polish word Rac, meaning Serb (as in the person from Serbia). So in Poland of the early 16th century "Rac cavalry" and "hussars" would be synonymous until Batory's reforms. Afterwards, they would be also called cossack or lisowczyk , with latter dominating after Cossack Uprisings throughout 17th century, also as mentioned earlier.