The button represented by <asp:Button runat="server".../>
will be converted to a web server control with a rich state model and different properties and methods which has more clear representation in real world like Button.Text = "Click Me".
The button represented by <input type="button" runat="server"..../>
will be converted to html server control represented by HtmlInputButton; with has limited properties, methods and events. Most of the properties resemble the html equivalents like Button.Value="Click Me".
Note that elements in a markup page are pre-processed/compiled before being used and will be converted to a class representation where every element is represented by a control. You can access server side controls which are identified by the runat="server" tag from the code behind since they will have the correct matching server control(web/html), other static content including an <input type="button.../>
tag with out the runat="server" will be represented as a LiteralControl.