Thank you for the question. It's actually quite a good one to ask, because a lot of people assume all karate is basically the same. And that's not true.
There are 3 main branches of karate in my perspective (there are actually more, and I'll mention that later):
- Japanese karate (Shotokan derivatives)
The Shuri-Te and Naha-Te lineages come from Okinawa. The Japanese karate lineages stem mostly from Shotokan karate, though there was often some cross-pollination going on with Okinawan karate and classical jujitsu, so it can be a little muddy with different styles of Japanese karate.
The thing to realize is that Shotokan karate popularized the art. It was brought from Okinawa to Japan in the early 1920's by a man named Gichin Funakoshi. He studied Shuri-Te versions of Okinawan karate and modified them to be taught in the public school systems of Japan as a form of exercise to school children. He called it Shotokan karate.
The Japanese school children eventually grew up, went to universities where they formed Shotokan karate clubs, and later formed their own Shotokan karate dojo all over Japan. That happened by around 1935.
During this same time period, Korea had long since been occupied by Japan, and young Koreans were drafted into the Japanese military. In Japan, Korean soldiers would be exposed to various Japanese martial arts, including Shotokan karate. They eventually returned home to Korea, where they formed Tangsoodo, Taekwondo, and other Korean versions of a karate derived from Shotokan karate.
At the end of World War II, American GI's were stationed in Japan where they were first exposed to Shotokan karate. They would bring Shotokan karate back to the U.S. where it would take off like wildfire in the early 1950's and 1960's.
By this time in the 1960's, Shotokan karate had multiple splinter organizations and different styles derived from it all over Japan. And it had spread across the world.
In the 1970's we saw the rise of Korean karate and its near total domination in the 1980's across the world. Taekwondo became one of the most popular martial arts in the world, if not the most popular. It was and still is based on Shotokan karate.
American Kenpo (Ed Parker's style) came out of karate and kung-fu styles in the 1960's and 1970's. It briefly surpassed Shotokan karate in terms of popularity, but it never reached the level of popularity that Taekwondo obtained.
There's Chinese Kempo also. And there's a number of other less popular forms of karate out there as well. I won't go into all of them.
Oh, and just to note: There's a third branch of Okinawan karate called Tomari-Te. The thing to realize is that Tomari-Te has pretty much died out. There's not a lot of pure Tomari-Te kata out there today. Most of the styles that purport to have come from Tomari-Te are actually mostly based on Shuri-Te. That leaves only Naha-Te and Shuri-Te lineages.
You can read more about the 3 main branches of Okinawan karate here: https://en.wikipedia.org/wiki/Okinawan_martial_arts
Now let's answer your main question: Which styles of karate are more focused on developing physical fitness and self-defense, rather than sport?
The short answer is: Okinawan karate. And in my opinion, specifically Naha-Te. And if I had to choose one branch of Naha-Te, I'd probably stick with Goju-Ryu.
Again, Japanese karate was developed by Gichin Funakoshi for school children as a form of exercise. It was modified in many ways to remove the martial qualities. The self-defense knowledge is almost completely missing in Shotokan karate and its derivatives, because it just wasn't taught.
Funakoshi didn't want kids hurting themselves with it. So he wasn't going to teach them what was really going on in the kata. And even things like the way punches are done in Shotokan karate made it hard for kids to hurt each other with it (the difference between a full-twisting punch in Shotokan vs. the 3/4 twisting punch of Shorin-Ryu karate).
Shotokan and its derivatives do not practice practical self-defense. They don't do partnered kata training and analysis, known as "bunkai" in Okinawan karate. So there is no connection between the kata and self-defense in these branches of karate. They will do sparring, but the sparring is not the same as self-defense.
I explain this more in detail at my answer here: Why is more time dedicated to exercises and very less for sparring? Is it for the fee?
Don't skip that link. Read it.
Now, Shorin-Ryu (Shuri-Te) is a very popular form of Okinawan karate. Depending on the teacher, you might hit the jackpot in terms of what they can show you in terms of practical self-defense coming from the kata themselves.
But as I said above, my own personal opinion based on my experience is that Goju-Ryu (Naha-Te) will give you a more well-rounded system of self-defense and physical development.
Kata bunkai is an integral part of Goju-Ryu also. Whereas Shorin-Ryu is more long-range, Goju-Ryu is more close-to-mid-range. There are shorter stances in Goju-Ryu. It's more obvious that there is grappling going on in the kata (Shorin-Ryu makes it all look like punches and blocks to a much higher degree than Goju-Ryu does). The use of the open hand as opposed to a closed fist is more prominent in Goju-Ryu. And Goju-Ryu has more circular movements than Shorin-Ryu does (a give-away that there's grappling going on).
As for physical development, Goju-Ryu takes it up a notch. In all karate schools, there will be physical development. That's true even in Japanese karate. But Goju-Ryu has its own unique system of physical exercise and conditioning, known simply as "hojo-undo". Hojo-undo is a common term that just means "supplemental exercises" (also known as body conditioning exercises).
You can read about some of Goju-Ryu's hojo-undo methods here: https://www.ftmaagojuryu.com/hojo-undo---supplementary-exercises.html
One of Goju-Ryu's most famous kata is called "Sanchin Kata". It's one of the first forms you're taught. It contains only a small number of movements. They're all done using dynamic tension and coordinated breathing. This dynamic tension is a kind of isometric exercise that will improve muscle tone and bone strength. The kata also packs a good amount of self-defense knowledge that forms the foundation for the rest of the style.
You'll find that Uechi-Ryu shares a lot of the same ideas as Goju-Ryu as well. It's also a Naha-Te style, so it shouldn't be too surprising. If you don't see Goju-Ryu being taught anywhere near you, you might want to see if Uechi-Ryu or any other Naha-Te lineage is taught near you. Failing that, a Shuri-Te branch of karate such as Shorin-Ryu might be your best bet.
If you can't find Okinawan karate near you, if the types of karate schools near you don't look like they're training practical self-defense, or if they seem to have an unusual number of overweight black belts, then you might want to consider doing something other than karate altogether.
In fact, I strongly recommend giving serious thought to training in Gracie Jiujitsu, Catch Wrestling, Sambo, Muay Thai, and/or MMA. These are styles that are heavily focused on training for self-defense and for body conditioning. If you want a no-nonsense approach, that's it. There are no kata to learn and no "interpretation/analysis" (bunkai) needed. They just cut to the chase and give you practical knowledge in a logical, straightforward manner. And in most cases with those styles, you're going to get a much more modern way of conditioning your body based on the best available understanding we have.
I think by now you've got your answers. Post follow-up questions in the comment section if you have them.
Hope that helps!