Today, the correct word is "older." I think in archaic English, sons and fathers (or other male relatives?) with the same first name were distinguished by "the greater" and "the younger." Such as, "James the Greater" and "James the Lesser" or "James the Younger." So,if you find the expression "the greater" in older texts, such as certain versions of the Bible, you are correct that this means "the older." However, this is not correct in today's English.