.aspx vs .ashx MAIN difference

.aspx is a rendered page. If you need a view, use an .aspx page. If all you need is backend functionality but will be staying on the same view, use an .ashx page.

Page is a special case handler.

Generic Web handler (*.ashx, extension based processor) is the default HTTP handler for all Web handlers that do not have a UI and that include the @WebHandler directive.

ASP.NET page handler (*.aspx) is the default HTTP handler for all ASP.NET pages.

Among the built-in HTTP handlers there are also Web service handler (*.asmx) and Trace handler (trace.axd)

MSDN says:

An ASP.NET HTTP handler is the process (frequently referred to as the "endpoint") that runs in response to a request made to an ASP.NET Web application. The most common handler is an ASP.NET page handler that processes .aspx files. When users request an .aspx file, the request is processed by the page through the page handler.

The image below illustrates this:

As to your second question:

Does ashx handle more connections than aspx?

Don't think so (but for sure, at least not less than).

.aspx uses a full lifecycle (Init, Load, PreRender) and can respond to button clicks etc.
An .ashx has just a single ProcessRequest method.