These two are the same word, the first in Sanskrit (as a native word) and the second in Japanese (as transliterated). But when Americans read these two spellings, they have a unique take on it.
"Look at how the Japanese mangled Sanskrit! 'Sowaka' is not even close to 'svaha.' " I've listened to this opinion expressed many times over the years, and now wish to point out that the opinion is ignorant and ethnocentric.
We in the US pronounce both spellings as if they were English words, and that's why the sound is so different. But do this if you can: listen to a speaker fluent in Sanskrit pronounce "svaha." (There are about 10,000 such people, including Dr Sharma, now retired from teaching the language at UC Berkeley, of whom I have a tape of his pronunciation.) Next, listen to a native speaker of Japanese say "sowaka." It is nearly identical to the Sanskrit.
It is amazing that even though there was an absence of cultural exchange for a thousand years (850-1850), the pronunciation has been passed down intact in Japan.