SquirrelMail and RoundCube are just web applications that act as clients to
an email server... no different than Eudora or Thunderbird or Outlook, except
that they run on a web server. To use a postal analogy, this is the
"Mailbox".
In order to actually send and receive mail, a mail service (server) is
required to which the client can connect. This server handles the
sending/receiving/storage of the messages. To continue the postal analogy,
this would be the "Post Office".
An email service may use a web based client such as RoundCube to provide
users with a way to access their mailbox over the web... however in that case
RoundCube itself is not the email service (server) it is just the interface
for accessing your messages. In your cited example, "OpenMailBox" would be
the email service with respect the question in the OP.