Does the same connection string used on two different physical servers hosting different web applications that talk to the same database draw connections from the same connection pool? Or are pooled connections confined to at the application level?

I ask because I inherited a 7 year old .NET 1.1 web application which is riddled with in-line SQL, unclosed and undisposed sql connection and datareader objects. Recently, I was tasked to write a small web app that is hosted on another server and talks to the same database and therefore used the same database connection string. I created a LINQ object to read and write the one table required by the app. Now the original .NET 1.1 app is throwing exceptions like

"Timeout expired. The timeout period elapsed prior to obtaining a connection from the pool. This may have occurred because all pooled connections were in use and max pool size was reached."

Maybe these are unreleated, but wanted to get your opinions to make sure I cover all my bases.

Thanks!