"Tuna fish" is a phase used primarily for canned tuna, but not for the live fish or things like tuna steak. It's because when canned tuna was created in the US in the early 1900's people who were not right next to the sea (like the majority of the US) did not know what "tuna" was. Firstly, the word is a of Spanish origin and secondly, its a salt water only fish. So in order to sell this to middle America, which was where most of the consumers were at the time but was also made up of people who have never seen the ocean, they added the word "fish" to show like other tinned fish that was commonly purchased: codfish, bluefish, and whitefish, this is also a fish and that is what you can expect when you open this can.

Colloquially tuna fish refers to the shredded salt brined tins of fish like this:

Which I do think is worth distinguishing from the actual whole pieces of tuna

There's no one single reason, but the top theories:

1. Tuna oil was a thing before "tuna fish". Yes, people could have said "tuna" but they didn't. That's language for you. People say "ATM machine" and "PIN number", too.
2. "Tuna fish" has a slightly sing-song pattern to the stressed/unstressed syllables that probably contributed
3. For whatever reason, "tuna fish" tends to refer to canned tuna, whereas "tuna" can include fresh (or frozen) tuna.

It's… just how language evolves.

I think, however, that "tuna fish" is slowly dying out in favour of just "tuna". As a 50 year old, anecdotally I have seen the usage decrease in my lifetime.

I bought some tuna fish and chai tea with cash i got from the atm machine

As an American who was only ever said tuna or tuna sandwich, etc. I do think "Tuna fish" has an appealing flow (euphonious consonants without any blends) and the ish pairs well with ich in sandwich

In my mind, tuna fish is the shredded stuff in a can and tuna is bigger pieces

Tuna fish is the chicken bird of the sea water.

You can twist knobs on a guitar, but you can't make it drink.

Well, where I live, Tuna is also a cactus. Prickly pear is often called tuna. So yeah, tuna (fish) and tuna (fruit) can need disambiguation.

Some of you have never eaten tuna cow and it shows

Horse back riding

If you don’t specify, Americans will ride the wrong part of the horse

If we didn't say that, we wouldn't have the joke about the difference between a piano and a fish.

I think it's mostly for the dad joke:

You can tune a piano, but you can't tune a fish.

A Czech reporter's name is Jan Tuna. Please keep saying "tuna fish" for his* sake.

* he/him, Jan is a common male name here derived from John, the female counterpart is Jana

What's the difference between a tuna and a piano?

This entire thread is /c/badlinguistics.

Don't want to confuse it with a guitar tuna

The opposite of "cow steak"

We have to specify so that Jessica Simpson doesn't get confused with Chicken.

Tuna is just the dish, tuna on a plate.

Tuna Fish is actually Tuna Salad. You would order a tuna fish sandwich (tuna salad), but you would not go to a restaurant and say "I will have the tuna fish" because that is just tuna.

Tuna was not always popular and when people didn't know what it was it helped people know what they are buying. The US also having a large portion of bilingual people with a Spanish base, this helps it not get confused with cactus fruit (apparently tuna in Spanish)