Calcola i giorni lavorativi totali tra due date

Se desideri escludere solo i fine settimana, puoi semplicemente escluderli utilizzando un conteggio condizionale aggiungendo:

count(distinct case when datepart(weekday, getdate()) <= 5 then date end)

Quindi la tua domanda diventa:

set datefirst 1;

select  count(distinct(dateadd(d, 0, datediff(d, 0,checktime)))) as workingdays,
        count(distinct case when datepart(weekday, getdate()) <= 5 
                            then dateadd(d, 0, datediff(d, 0,checktime)) 
                        end) as weekdays
from departments,
 dbo.USERINFO INNER JOIN dbo.CHECKINOUT ON 
     dbo.USERINFO.USERID = dbo.CHECKINOUT.USERID
where  userinfo.name='Gokul Gopalakrishnan' and deptname='GEN/SUP-TBL' 
and checktime>='2014-05-01' and checktime<='2014-05-30'

COMUNQUE Consiglio vivamente di aggiungere un tabella del calendario al tuo database. Rende tutto così semplice, la tua domanda diventerebbe:

SELECT  DaysWorked = COUNT(cio.Date),
        WeekDaysWorked = COUNT(CASE WHEN c.IsWeekDay = 1 THEN cio.Date END),
        WorkingDaysWorked = COUNT(CASE WHEN c.IsWorkingDay = 1 THEN cio.Date END),
        TotalDays = COUNT(*),
        TotalWeekDays = COUNT(CASE WHEN c.IsWeekDay = 1 THEN 1 END),
        TotalWorkingDays = COUNT(CASE WHEN c.IsWorkingDay = 1 THEN 1 END)
FROM    dbo.Calender AS c
        LEFT JOIN
        (   SELECT  DISTINCT
                    Date = CAST(CheckTime AS DATE)
            FROM    dbo.Departments AS d
                    CROSS JOIN dbo.userInfo AS ui
                    INNER JOIN dbo.CheckInOut AS cio
                        ON cio.UserID = ui.UserID
            WHERE   ui.Name = 'Gokul Gopalakrishnan' 
            AND     d.deptname = 'GEN/SUP-TBL' 
        ) AS cio
            ON c.Date = cio.Date
WHERE   d.Date >= '2014-05-01'
AND     d.Date <= '2014-05-30';

In questo modo puoi definire giorni festivi, fine settimana, ecc. È molto più flessibile di qualsiasi altra soluzione.

MODIFICA

Penso di aver frainteso i tuoi criteri originali. Questo dovrebbe funzionare per te senza una tabella del calendario:

SET DATEFIRST 1;

DECLARE @StartDate DATE = '2014-05-01', 
        @EndDate DATE = '2014-05-30';

DECLARE @Workdays INT = 
    (DATEDIFF(DAY, @StartDate, @EndDate) + 1)
    -(DATEDIFF(WEEK, @StartDate, @EndDate) * 2)
    -(CASE WHEN DATEPART(WEEKDAY, @StartDate) = 7 THEN 1 ELSE 0 END)
    -(CASE WHEN DATEPART(WEEKDAY, @EndDate) = 6 THEN 1 ELSE 0 END);


SELECT  WorkingDays = COUNT(DISTINCT CAST(CheckTime AS DATE)),
        BusinessDays = @Workdays
FROM    dbo.Departments AS d
        CROSS JOIN dbo.userInfo AS ui
        INNER JOIN dbo.CheckInOut AS cio
            ON cio.UserID = ui.UserID
WHERE   ui.Name = 'Gokul Gopalakrishnan' 
AND     d.deptname = 'GEN/SUP-TBL' 
AND     cio.CheckTime >= @StartDate
AND     cio.CheckTime <= @EndDate;