Explain any case in which

Hi Manpreet,

Action Support Tag in apex,supports "event" attribute which makes the ActionSupport to add AJAX support to another visualforce component and then call the controller method.For E.g.

<apex:outputpanel id="outptpnl">
<apex:outputText value="click here"/>
<apex:actionSupport event="onclick" action="{!controllerMethodName}" rerender="pgblck" />
</apex:outputpanel>

Here action support adds AJAX to output panel, so once you click on output panel controller method will be called.

Whereas,Action function cannot add AJAX support to another component. But from a particular component which has AJAX support(onclick, onblur etc) action function can be called to call the controller method.
Example:

<apex:actionFunction name="myactionfun" action="{!actionFunMethod}" reRender="outptText"/>
<apex:inputcheckbox onclick="myactionfun" />

Hope this will help You.