Adding 해 to ~야 adds a verb. 비가 그쳐야 해. (The rain has to stop.) If you were to remove 해 from the sentence it(비가 그처야) would no longer be a complete sentence because it lacks a verb. 비가 그쳐야 놀러갈 수 있어. (The rain has to stop in order for us to go play.) This is a complete sentence because a verb’s been added again. As for the two sentences, yes, they mean the same thing. Their difference is similar to its counterparts in English. I have to speak Korean well to live comfortably in Korea. To live comfortably in Korea, I have to speak Korean well. ~어야 is a requirement, essentially. Just as a reference, 2nd sentence: 한국에서 편하게 살려면 한국말을 잘해야 해요. 한국에서 살기 편하려면 한국말을 잘 해야 해요. These are better sentences. Still, the original sentence IS understandable, so no need to care too much :)

어야 connects two things meaning one needs to be in order for the next thing to happen. -야해 means a (one) verb has to be done. 해야해=gotta do it.