Factual error: In the 1996 sequence the kid is playing a PlayStation with DualShock controllers, those controllers weren't released until 1997.
Factual error: When Alex gets bitten by a mosquito (one of his weaknesses) and Bethany saves him. They venture off into the jungle to find the statue, so there was only 1 mosquito in the jungle? A jungle is full of mosquitos.
Answer: The Van Pelt seen in the sequel is a 're-imagined' version of Van Pelt due to the fact that Jumanji has evolved to become a video game, rather than a board game.
Same character, alternate universe.