Why is the guitar called violão in Portugal and Brazil?
Tar means string in Proto-Indo-European and Sanskrit. Instrument names like kithara and guitar have this word in it.
The kithara was a classical Greek large lyre.
Cithara is Latin for lyre, and in the renaissance it was used for lute, as well.
Words like citole/citula/cistern/gittern referred to medieval European wire-strung instruments derived from the classical Roman fretted instrument.
Cittern arose from this tradition by the 16th century. The 18th century English guittar was a cittern. It traveled to Portugual via sea trade and became the guitarra portuguesa. I I don't think it made it to the new world, though other citterns did, called mandola or bandola.
The guitarra latina and guitarra morisca (pictured) were medieval instruments of Spain, the former being the citole from the Roman Empire and the latter being the qanbus/gambus from the Moorish conquest of Andalusia.
The guitarra italiana was a 16th century lute with a longer neck. Lutes were ouds brought to Spain by Moors. Arabic "al'ud,' meaning "the wood" or "the fragrance" became laúd (Sp), luth (Fr), liuto (It), lute (En), etc.
The chitarrone of 17th century Italy, aka the theorbo, was literally a big chitarra (italiana). It was also used as a humanist symbol to replace the lyre or kithara of the classical Greek lyric poets. Thus, it is also symbolically a big kithara.
Todya's guitar took on its familiar waisted shape in 14th century Spain and France. Its rosette was Arabic, not like the citole's and gittern's, which were Gothic. To me this indicates its Moorish origin. Before that, I don't know, though I did find its tuning in an 11th century Persian oud treatise. That may be coincidence.
All Latin American guitars are derived from European ones. The Hawaiian ukulele that the Portuguese brought over, the cuatro venezolano and the Mexican jarana jarocha retain some of its old character from the 16th and 17th centuries.
These images are from the Cantigas de Santa Maria, a medieval Spanish songbook.
These are vihuelas. Left is a vihuela de arco (bowed viol) and right is a vihuela de peñola (plectrum viol).
Vihuelas in Spain and viols in Italy were played da gamba (held by the legs) by the 15th century. The viola da gamba survives as the double bass viol (the orchestral contrabass).
The violin family took shape in 16th century Italy: violin (small viola), viola, violoncello aka cello (little big-viola), violone (big viola). In the 16th and 17th century, violone was a broad name for any large bowed viola. The double bass that survives to the present is part of the viol family (viola da gamba), not the violin family (violin, viola, cello).
In 16th century Spain and Italy, a waisted, flat-backed instrument called the vihuela de mano/viola da mano was used as an alternative to the bowl-backed lute. In Spain the lute/oud had Islamic connotations, and the vihuela Christian ones.
Portuguese, and subsequently Brazilians, called our guitar the violão. That name comes from this medieval tradition.
So: the words guitar and viol have both been applied, across different languages, to the instrument family now commonly known as the guitar. But, the word guitar also historically applied to citterns, and still does in Portugal, and the word viol used to be applied to guitar-like instruments, and still does in Portugal and Brazil.