I am a salaried exempt employee in MS. My company's policy is to pay overtime and comp time to the exempt and non-exempt employees....at the manager's discretion. Different departments have different rules concerning the actual earning of any overtime or comp time. My manager's rules is that we may not accrue any OT or comp time until after 9 hours are worked per day. For other departments it is anything over 8 hours per day.
Also, if we are out for any reason (sickness or doctor's appointment) we must use the comp time that we have worked in the past cover the time off. It seems like the policies are contradictory; that the rules of exempt and non-exempt are both being used.
What are the true regulations for exempt overtime in MS?

There are none; in MS or any other state. An exempt employee is not entitled by law to overtime under any circumstances whatsoever.

If the employer chooses to offer either comp time or overtime to exempt employees, that is entirely their choice and it is entirely up to them how to apply it. It is not illegal for them to do it differently by departments.