Extenders enable you to customize and extend the capabilities of ASP.NET controls without having to create new classes.
There is no calendar extender, instead a calendar of Ajaxtoolkit is a kind of textbox extender where textbox has additional behaviour of calendar.
Standard calendar control is a one single control having a defined behaviour. Calendar of AjaxToolkit is a textbox control extended to a level(with a given behaviour) that can be used for picking dates via claendar.
Refer: Creating a Custom AJAX Control Toolkit Control Extender (C#)