Oceanic white tips and Tiger Sharks are man eaters, they have been know to stalk, hunt and consume humans. They will return to devour a human. The meme that Sharks do not eat humans is not entirely true, but the reality is they prefer other meals. Well at least the tiger shark does. Oceanic white tips are the piranhas of the open ocean, they eat everything they come across. It is a good thing they only live in open ocean as if they where a shallow water shark there would be far more shark attacks.
I spearfish, and have spent a lot of time in the water with sharks. There nature is very much like that of dogs. If you show fear, try to flee and basically make yourself look like prey they will get attracted. If you stand your ground, give them a nudge to the face when they get to close. They see you as a competing apex predator that can hurt them, sharks are adverse to fighting for their meal. It is why injured fish is such and attraction to them. I have been in the water with them, just cruising around not paying any attention to anything, someone shoots a fish and all hell breaks loose if you don;t get the fish up fast enough. Once you are in possession of the fish they act as if another shark got it and go back to just cruising around. If they get to your fish before you get it up, they will clean it off the spear in seconds flat.
In my few encounters, Sharks tend to avoid any dolphin species including porpoises and Bottle-nose. In the presence of humans it has been my experience that dolphins tend to be more aggressive towards sharks, running them off. I don't read too much into it, because I imagine they probably do the same when we are not around.
I would imagine that sharks compete for the same food source so they run them off to ensure food availability. Dolphins will also not try to steal your catch, at least not in my experience.
My expereince with dolphins is limited though, I have only been in a pod while spearfishing twice and both times where due to the fact that there was a bait ball, so there where a lot of predators competing for prey fish. Including Sailfish and Marlin, which the dolphins seem to use as the billfish bat thru the ball stun the fish and then the pod will grab some of the stunned fish.
My personal experience is that dolphins know what spearguns are, and don't like them, they generally don't approach if you are spearfishing. The release of a spearshaft and the band pop is a very distinct vibration, many apex fish including large grouper and sharks are keyed into it, in some areas. I remember one time, I pulled the trigger and had two blacktips on me within a split second. The fish was dead on impact so the only vibration was the gun going off. Anyways I would guess that dolphins key into this as well and avoid it.
That being said, when I am in the water without a gun they always approach check me out, push their babies towards me to check me out. I think it's akin to us going to sea world, it really is like hey kids look it's a human check it out, get a good look you don't get to see these too often.
One time my dog jumped in and the babies would swim about a foot under it, to make it go crazy barking. I think they loved the sound as when she would stop they would circle back and get her going again. (Side note: I think dolphins are into ASMR if you are ever in the water with them make sounds they love it). It was the one time I thought to myself, I hope dolphins don't eat dogs because she is a beagle, so small enough. Anyways, they don't, and I am glad they don't hunt humans, if they did we would not be able to enter the water. A human hunting dolphin would be a fearsome predator and absolutely terrifying in a serial killer kind of way. They are really smart and you get a feel for how smart they are when you have natural encounters with them.
I spearfish, and have spent a lot of time in the water with sharks. There nature is very much like that of dogs. If you show fear, try to flee and basically make yourself look like prey they will get attracted. If you stand your ground, give them a nudge to the face when they get to close. They see you as a competing apex predator that can hurt them, sharks are adverse to fighting for their meal. It is why injured fish is such and attraction to them. I have been in the water with them, just cruising around not paying any attention to anything, someone shoots a fish and all hell breaks loose if you don;t get the fish up fast enough. Once you are in possession of the fish they act as if another shark got it and go back to just cruising around. If they get to your fish before you get it up, they will clean it off the spear in seconds flat.