What is difference between web.config assemblies element and project file Reference element

I'm looking at an asp.net application, i notice that there are assemblies defined into two places. In web.config there is configuration/system.web/compilation/assemblies/add elements. In the project file there are references setup under the Project/ItemGroup/Reference elements.

I was wondering, what is the difference between assemblies/references added in either location?

In the web.config section:

The assemblies element defines a collection of assembly names that are used during compilation of an ASP.NET application.

Web site projects usually use the assemblies element as there is no project file storing location of references that the web site uses. The project references would not apply to a web site, as it has no proper project file to store these in, so must store all referenced assemblies in the web.config. There is some interesting, although not directly related, discussion here.

Web application projects may make use of both the assemblies element and project references.

Having a reference in the assemblies element also means you won't have to add the @register at the top of any .aspx pages that use that namespace. More discussion on that here.