In Jurassic World, after defeating the Indominus Rex, the T-Rex and Velociraptor exchange a glance and then leave different ways. Was that really a natural behavior?
Considering these are not real T-Rex or Raptors (in universe, states to have been manipulated to fit the public imagination of what dinosaurs should look like), not knowing how much they are manipulated, them not being natural competitors due to time periods, etc, the simplest answer is that we can't tell.
Now ignoring that, we can guess based on modern day animal behavior. There are many animals, prey, predators, or even apex predators that will occasionally team up for various reasons. Even ones that will normally be aggressive and fiercely territorial. One pair that is typically documented are bears and wolves (very apt analog for Rex and Raptor). When environmental pressures are relaxed, they will not attack each other unless needed. They will even share a meal (insert picture of wolves and bears eating a beached whale here). A mutual enemy, when retreat is not an option, would be reason enough to team-up, in a anthropomorphic sense.
There are also plenty of instances of normally aggressive animals raising the young of others, or becoming friends in both domesticated and wild situations.
As for the movie, it can be boiled down to "You're no threat and I'm not hungry" on the T-Rex side, and "Your too big for me, your not attacking, and I'm not hungry" for the Raptor. Mutual disinterest as opposed to "respect" or any typically human emotion. The main consideration being threat, almost wholly dependent on size. A lone tiny Raptor is to a Rex like a Chihuahua to a Human.
I think it was just a way of showing the (albeit temporary) bond that they developed during the fight. Don't think the writers meant for the audience to read much into it.
T-Rex : "Dude, thanks for helping me out there. High five. Now get the hell out of my face; I've had enough shit for one day"
Velociraptor : "See ya around big guy" * zips away *
I did some checking after my comment and found that T-Rex (fossils are found in a variety of rock formations dating to the Maastrichtian age of the upper Cretaceous Period, 68 to 66 million years ago, wiki) and Velociraptors (lived approximately 75 to 71 million years ago during the later part of the Cretaceous Period, wiki again) did not lived on the same period of time.
Also a T-Rex has a speed of roughly 18mph while a Velociraptor run up to roughly 40 mph (too fast for a T-Rex, wiki), and Velociraptors hunt in packs (specified in the movie).
Now referring to the movie T-Rex sees Indominus Rex they growl, no one backs up so they both attack (natural behavior to me). The Velociraptor follows Owens command and also attacks. After that fight there is no reason to fight each other, none of them display aggressive behavior towards the other.
Rexy fought the raptors in Jurrasic park but not the ones in Jurrasic world because they did not exhibit agressive or challenging behavior towards her. In fact they fought alongside her against the unnatural hybrid.
In this video a paleontologist answers this exact question, in summary, it is not likely dinosaurs understand the concept of "help". There is no reason for the raptor help the T-Rex to begin with.
Tyrannosaur rex named Rexy was fighting against the Indominus because she was lured by Clair but her strength proven she was no match until nearly death saved raptor a common old enemy from her past that she killed named the big one and her minion. Though she understand be out of her captivity that raptors are enemy but since their were only three but she had killed two and the other one was frozen to death she became the queen of Isla nubler. With no real large predators but herself seems to think she the strongest until she met the I.rex but saved by Raptor as team to kill the evil threat made her realized that Raptor named blue had back off to show some respect to each other mostly moral reason. So rex quickly understood Blue as raptor isn't so much of threat compared her first time woth raptors 22yrs ago.
Its just a dramatic anthropomorphic moment, the kind you see two incompatible heroes have at the end of a movie just before parting ways after a brief period of collaboration to bring down the evil guy. Something like the final scene of
Mad Max Fury Road.
There is no possible answer even though the velociraptor and the tyrannosaurus rex were the two most feared dinosaurs the last velociraptor died 10 million years before the first tyrannosaurus was even born.