Spider-Woman had already been a prominent Marvel character for years by the time “Secret Wars” kicked off in 1984. Her real name was Jessica Drew, and her costume was a bright collage of reds and yellows. In “Secret Wars,” Marvel introduced a brand-new Spider-Woman in the form of Julia Carpenter. When she enters the scene for the first time, she sports a stylish black-and-white outfit that instantly sets her apart from her predecessor.
Spider-Man’s black suit also originated in the “Secret Wars” storyline, though it wasn’t until later that Peter Parker discovered the true nature of the symbiote. Peter wonders at the time why the strange goo he finds changes the colors of his costume so significantly, and he decides that he must have been subconsciously influenced by Julia’s suit during the process.
So, in a way, Julia’s suit is a Venom symbiote suit, in that it may (or may not?) have served as inspiration. Of course, at the time of “Secret Wars,” no one at Marvel could have possibly imagined how popular Spider-Man’s new look would be or the many, many new characters who would spawn from it. In “Madame Web,” Julia’s suit is, in all likelihood, just a regular costume.