What is the difference between a connection and a session?
The connection is the physical communication channel between SQL Server and the application: the TCP socket, the named pipe, the shared memory region. The session in SQL Server corresponds to the Wikipedia definition of a session: a semi-permanent container of state for an information exchange. In other words the sessions stores settings like cache of your login information, current transaction isolation level, session level SET values etc etc.

Normally there is one session on each connection, but there could be multiple session on a single connection (Multiple Active Result Sets, MARS) and there are sessions that have no connection (SSB activated procedures, system sessions). There are also connections w/o sessions, namely connections used for non-TDS purposes, like database mirroring sys.dm_db_mirroring_connections or Service Broker connections sys.dm_broker_connections.