Giant Spider is a blanket-term used for any spider that has been infected due to the t-Virus in an unplanned manner - an "irregular mutant". They are different from the Web Spinner in the sense that the Web Spinner B.O.W.s were experimented from the start, while the wild spiders simply mutated on contact. The Giant Spiders, like other t-Virus-infected spiders, produce "little spiders", which live on their mother's back. If the back of Giant Spider wasn't blasted by powerful weapons, Little Spiders won't appear. Unlike the Web Spinner, these "irregular mutant" spiders had kept the ability to create a web for trapping prey, which logically, made them much more akin to the Black Tiger.
The Giant Spiders frequented in the sewers of Raccoon City, where they were infected during the Raccoon City Destruction Incident when the t-Virus was leaked into the sewers. In a similar manner, Giant Spiders populated the sewers of Sheena Island two months later during its own viral outbreak, when t-Virus -laced chemicals mixed into the sewage.
Like other spider-like creatures in the series, those species can poison the player by spiting fluid on him. Blue Herb plantations are the warning sign to player, that he or she must be ready to encounter those poisonous spiders.
Claire escaping from a Giant Spider in Resident Evil 2
A Giant Spider attacking Jill in Resident Evil 3: Nemesis