What differences exist between the pay and free version of MSSQL2008R2?
Microsoft SQL Server 2008 R2
http://www.microsoft.com/sqlserver/2008/en/us/R2.aspx
and Microsoft SQL Server 2008 R2 Express
http://www.microsoft.com/express/Database/
A complete answer might explain why someone would choose one over the other, what the biggest annoyances are with going Express, non-intuitive things to look out for, etc.
Best Answer
Executive summary (Commonly missed features for the person running a small database):
SQL 2008 R2 Express edition is lacking:
SQL Server Agent (for scheduling jobs, including SQL replication)
support for DBs >10GB
Integration services
There are many other differences, detailed at the URL Moose posted.
SQL Express CAN be accessed from the network, but it is not enabled by default. A quick google will show how