The 2 queries will give same result if ConnString column is NULL because
NULL + Anything is NULL.
To see the difference between 2 queries use
ISNULL[
^]
Try
SELECT DBName, ISNULL(ConnString,'') + '#VIJAY#' + ISNULL(FinanceConnString,'') + '#VIJAY#' +
ISNULL(RptDBConnString,'') AS ConStr FROM [DataBase] WHERE Active = 1