No, but SSE has a number of options turned on that are typically not on in higher versions of SQL Server. You could turn them on but wouldn't want to if you are using SQL Server as a general server, not a local database store. In addition, there is some behavior that is unique to SSE that is particular to the way local database stores are used.
You can install multiple instances of SQL Server (2k, 05, Express or otherwise) on the same machine. Each instance has a name that is specified during install. You can also have 1 default instance.
By default, VS installs SQL Express with an instance called SQLEXPRESS. For the database connection thing to work in VS it needs to know the name of the instance. From the server explorer you can create a connection to any database and you get the oppurtunity to specify the server name and instance.
Go in VS2005 into "Tools | Options | Database Tools | Data Connections" and in the Connection Options there's a textbox labeled "SQL Server Instance Name (blank for default):".Enter SQLEXPRESS into this field.