Berber, nomad or stretch tent: one family
According to the site's product page, the stretch tent is a structure made of bi-elastic polyester fabric tensioned over adjustable poles. “Berber tent” refers to the inspiration of the nomadic tents of the Maghreb, with curved shapes and a sense of travel; “stretch” describes the technique. When you compare quotes, check the product rather than the name: a Berber tent and a nomadic stretch tent are, most often, the same thing.
For a comparison with the marquee and the aluminium structure, read the article on choosing between a stretch tent, a marquee and an aluminium structure.