In short: those are pretty much the two only solutions.

Of course, there are different types of depression and they can all be cured in different ways. For some of them there's no cure at the moment.

Matter of fact I had seen a study that suggest a very high percentage of people are drug treatment resistant (meaning that there depression would not get better with any prescribed drugs).

Therapist =/= drugs. First of all, a therapist cannot prescribe you anything. That's the job of psychiatrists. Both a therapist and a psychiatrist may recommend drugs for depression if they deem it appropriate, but it's by bo means the default or the go-to option (or at least it shouldn't be). Sometimes depression is a natural response to events like death of loved ones and drugs do nothing to cure it.

I had seen studies that say that training or even just daily walks can highly improve mood, but I had never heard that they fully cure depression.

Both of those things are commonly recommended by regular people as well as therapists, because they're known to be effective, and more importantly - they are completely free. For 99% of people, absolutely nothing is stopping them from doing a few pushups or walking to a park. The cost/benefit ratio here is insane. As for 'fully curing depression' - that would highly depend on the type of depression. Also, keep in mind depression is rarely cured with just one thing.

To summarize: people recommend a therapist, because a therapist is usually the best option for any mental problems, though it may not be cheap. While exercising, or just walking and interacting with nature, are basically free and always help, but may not produce noticeable results.