Connect authority allows one entry to the database environment.
Access authority defines the permissions the user has to operate within the enviropnment (i.e read tables, update tables, etc).
You might think of it as a building with a "front door" and many doors in the halls inside the building. "Connect" would be the key to the front door allowing entry to the building. "Access" would be the keys to open the interior doors once one had gotten thru the front door.
Hope this helps,