Mail.app: connect to IMAP server with STARTTLS
First of all, notice that port 993 usually does not use STARTTLS. If you have been told to use port 993 and STARTTLS, then that would be very strange indeed. The different between STARTTLS and ordinary SSL/TLS is the following:
With ordinary SSL/TLS, which is what is usually used on Port 993, the connection immediately starts with an SSL/TLS handshake. In layman's terms, one may say that the connection is immediately encrypted. However, when using STARTTLS, which is usually used in combination with Port 143, the connection starts unecrypted. The first IMAP commands exchanged between client and server (including the STARTTLS command) are unencrypted. However, after the STARTTLS command, both client and server upgrade the unencrypted connection to an encrypted one. That means the SSL/TLS handshake is not done immediately, but only after the client has sent the STARTTLS command to the server. That's all.

Now sadly, I have experienced that Apple's Mail App does not support STARTTLS on Port 143 and seems to only support encrypted IMAP connections over Port 993 using SSL/TLS.