Is there a difference in the meaning between the words Hallelujah and Alleluia? And if not, why are they spelled differently?
No, both words are the same. Hallelujah is a Hebrew word, ( הַלְּלוּיָהּ Hallal (Praise) + Yah (The LORD). Hence “Hallelujah” means, “Praise the Lord!” But the exact way that the Hebrew letters are transliterated into English and other languages has varied a bit over time. Perhaps most influential is the fact that the Greek New Testament rendered the Hebrew word Hallelujah as ἀλληλούϊα (allelouia). And since Greek is generally more influential in English spellings than Hebrew, many English translations render the word as Alleluia.
However, not an insubstantial number of English translators have preferred over the centuries, especially when translating the Old Testament Hebrew, to render the term Hallelujah. Some translators will use Hallelujah for the Old Testament and Alleluia for the New Testament.
Music has also influenced the decision over which spelling to use since some of the famous compositions from the Baroque period, such as Messiah, used the spelling Hallelujah that was more common in earlier English translations of the Bible.
At the end of the day, it is the same word, just with different spellings.
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