why is it that some messages sent from classmates have message embedded in them when I receive them, but others require I go to the site to view in my Inbox?

They don't. All messages sent from the site only sent a notice to your regular email asking you to visit the site to retrieve your message.

Two exceptions to this that you may be seeing:

1) Messages from a site administrator (site wide emails) will come directly to your email box. You don't have to log into the site to retrieve those.

2) If you are communicating with a Classmate back and forth through the site, and one of you clicks respond on your regular email program rather than coming to the site, now you've just sent a message through your own email, outside of the site. This is pretty easy to do. Just click respond on any message notification, and your response is going to go directly back to the private email box of the Classmate who sent you the message.