Using a specific data type -- such a date or datetime -- only works on later versions of SQL that specifically check for that in the optimizer.
Best when dealing with singular values / variables is to use format 'YYYYMMDD', which SQL will always implicitly convert to the column's format, regardless of SQL version. Converting a few values is trivial as far as overhead. You wouldn't want to do this for a table with millions of rows:
table.date >= CONVERT(char(8), GETDATE(), 112) AND
table.date < CONVERT(char(8), DATEADD(DAY, 1, GETDATE()), 112)