You're conflating two different things that have the same name.  The shared server has:

1.  sendmail—a daemon running on the local host.  This daemon does two things:
a.  Receives incoming mail on port 25.  If the delivery address is local, it delivers it.  
Otherwise, it either relays it or refuses depending on whether credentials were provided by 
the connecting host.
b.  Looks for email in an outgoing spool folder.  It delivers this without asking for credentials.

2.  sendmail—a binary on the local machine that drops files into the mail spool.