Asynchronous manner,pull and push

Asynchronous has two ways:pull and push.

Here I want to know the difference clearly,
The following is my understanding:

the pull is :

1)client send request to server
2)server retrun the status to client,and the client request for stauts again and again unless it get the right status,then it will start to get the really response of the server.

It seems that the ajax use this manner,however I heard somebody say this process is related to the callback mechanism,I can not found where it is,anyone can tell me ?

And the push is:
1)client send a request with a response address to server.
2)server handle the request,and after completed ,it will return the response to the address.

Isn't it? if so, I want to know whether the connection of the client and server can break off between the step 1 and 2 ?
Also,what can be the response address like? a url or something else?
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Now I want to know if my understanding is right or not, enough or not, and I will appreciate someone can tell me more about it, since I am doing some asynchronous-related job in the web service domain, I need some guide , thanks.