When in 'SQL Server Configuration Manager' I see, under 'SQL Server Services', 2 items that look like SQL Server's:
Does that mean I have 2 versions installed at the same time? The 'SQL Server (mssqlserver) is currently stopped).
You have two instances. They might or might not be the same version (meaning 2005/2008).
Express is just an SKU / edition from the myriad of different editions.
You can have the same version or multiple versions/SKUs installed as different instances on the same machine.
So unless someone wittingly set up a new instance with the name "sqlexpress", you probably have two kinds of products installed (both can be 2008 or both can be 2005 or they can be different - it is just that one of them is presumably the Express SKU while the other is say Standard.)
You can get more information on the instances by using @@VERSION.
SQLExpress is the light/free edition, usually used for developers or very lightweight applications.
MSSQLServer is the full blown SQL install.
So yes you have 2 "SQL Server" installs, but they are different products, I can't say which versions based on your provided data.
You have two SqlServer instances installed on your system. One is SqlServer Express Edition and the other one a Sql Server. I can't say which version or edition.
Maybe you can find some more information in the registry (HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft).
It looks like you got SQL Server Express installed with Visual Studio and then later installed SQL Server 2008. I've done this before and the best solution I found was to completely uninstall SQL Server Express and SQL Server 2008. Remove all the files in the Microsoft SQL Server directory in Program Files, then reinstall SQL Server 2008. If you still have problems getting the 2008 instance to be the default, you may also need to uninstall Visual Studio.
In the future, if you're going to install the development (or other) version of SQL Server locally, I suggest making sure you install it before Visual Studio. The VS install won't install SQL Server Express if it detects an existing SQL Server instance on the system.
BTW, you can verify if this is true by using the Add/Remove Programs Control Panel item.
I'd vote against removing either one--SQL server does fine with multiple instances and they are good for different things. For example, lots of open source projects presume a local copy of sql express at .\SQLEXPRESS for development use. Whereas you can't write analysis service stuff with SQL Express.
Or, its not a problem. Those aren't the droids your looking for. Move along.