Which SQL Server version can connect to remote web server?

Question

Hi,

I see there's quite a few versions of SQL Server 2008.
One of those is the WEB version ("for web application hosting").
Does that mean I need that version in order to host a database which can be approached through the web/internet?

I have a DESKTOP application (C#) and I'm trying to get the data from my web server through the internet, but I get the following error message:

"A network-related or instance-specific error occurred while establishing a connection to SQL server. The server was not found or was not accessible.
Verify that the instance name is correct and the SQL Server is configured to allow remote connections. (provider: SQL Network Interfaces, error: 26 - Error Location Server/Instance Specified)"

In my web server I installed SQL Server 2008 Express and I can access the data internally (intranet) but it fails when using the (temporary) IP-address assigned by the internet provider and or the name assigned by the DynDns.
I have configured it to allow remote connections, but all to no avail.

Thus, back to my question, is the SQL Server 2008 WEB version required to access data through the internet?

Then, if the Express version should accomplish that task, what exactly is the advantage(s) of the WEB version, or how does it contribute to establishing the connection?
...and, assuming the Express is enough, what could I be missing (some setting, permission, etc.) that I cannot get it to work (accessing remote data)?

Thanks a lot in advance.