The movie adaptation of the beloved "Teenage Mutant Ninja Turtles" reportedly didn't receive good reviews for its premiere. The film's storyline was said to have differed a lot based on the original comicbook source. Even some character's origins were changed.
This article also contains spoilers for "Teenage Mutant Ninja Turtles." Read at your own risk.
The Ooze plays an important role in the origins of Splinter and the four turtles. Below is a comparison on how it was introduced in the movie against the comics.
Movie: Eric Sachs (William Fichtner) defined the mutagen as "extraterrestrial." According to Screenrant, this is hinted at the label on its canister where it reads T.C.R.I. (Techno Cosmic Research Institute). The institute based on the comics is actually Earth's home of the aliens called Utroms.
Comics: Similar to the movie, the ooze was created by T.C.R.I. specifically by the Utroms when they attempted to create a portal back to their planet. According to Comicvine the mutagen plays an important role in the turtle's mutation. One of the canisters containing the substance accidentally broke and the contents spilled into a sewer.
The turtles and Splinter's mutant origin:
Movie: According to Screenrant, the turtles and Splinter were "lab rats" in Sach's experiment with the ooze. The turtles were also April's pet. Together with her father Dr. O'Neil, they named them Donatello, Leonardo, Michelangelo, and Raphael. They also painted each turtle's shell with a dash of purple, blue, orange, or red to distinguish them from each other.
When April's father died, she rescued the four turtles and Splinter from the lab and placed them in the sewer. That's when Donatello, Leonardo, Michelangelo, and Raphael started to mutate and grow in size. Even after their mutation, Splinter treated them like his own sons.
The four "Teenage Mutant Ninja Turtles" were prohibited by Splinter to venture outside the sewer and into the streets of NYC. It was his way of protecting and hiding their identities.
Splinter also taught them how to do martial arts when they became reckless, something that he learned himself from an old guide book. However, Donatello, Leonardo, Michelangelo, and Raphael were too curious about the outside world that they ended up going behind their master's back.
The four "Teenage Mutant Ninja Turtles" ventured outside their hiding place from the sewer to secretly battle the members of the "Foot Clan." That's when they were discovered by April O'Neil.
Comics: The turtles mutation happened by accident. According to Comicvine Yoshi's pet rat discovered the ooze and the four little turtles while scavenging for food in the sewer.
The Utroms were transporting the mutagen on a truck when the vehicle got into an accident. The canister broke and its contents toppled a container containing four little turtles carried by a young boy. The turtles and the canister fell into the sewer.
The rat eventually rescued the ooze-drenched turtles, getting the mutagen onto himself as well. The next day he woke up to discover they all have grown in size. The turtles started to develop in intellect and learned how to speak. One even called the rat "Splinter."