The difference between these two terms is that one is related to mobile technology and one to the email and the process of sending emails:
SMSC stands for Short Message Service Center which is a network component used to deliver SMS messages. When a user sends an SMS using his/her mobile phone, then it is sent to this network component and then the server sends the SMS to the recipient when it is in the coverage area of the carrier’s networks. SMSC servers have to ability to save the SMS messages for when the destination is not available.
MAPI stands for Messaging Application Program Interface and it is a COM model used in the process of sending emails through Windows environment using different email clients. The MAPI interface takes advantage of the subsystem’s routines for the good communication with the email servers. The MAPI protocol is used by Outlook and Exchange application and servers.
So actually, there is no connection between these two terms.