Well in Hindi we use them together also. For instance - shaadi byah ka mamla hai. So it is not a different word, a synonym and even used together to mean - marriage.

Hello! I think though they have same meaning byah is used for the wedding ceremony where as shaadi is used for marriage as in general too. Neeta

Both are same

Not much difference But the major difference if I would say then that would be व्याह is kind of regional word people in the villages use this word. शादी Is very general world mostly recognize by people. Not matter where they belong Rural or Urban. https://www.italki.com/TeacherNikhil