That difference is intentional because the death of Bambi’s mom taught the director of The Lion King that they needed to show Mufasa’s demise for it to have an impact on Simba.
The difference between the deaths is that Bambi’s mom is shot off-screen by a hunter, while Mufasa is thrown off a cliff into a stampede of wildebeests and his son finds his corpse.
In Bambi’s case, it’s famously the little deer’s mother and in The Lion King, Simba’s father, Mufasa.
Other than solely starring talking animals, Bambi and The Lion King share something in common: they both feature the death of a parent during the course of the film.