Webhook is said to be push style communication which enables an application to push data to another application.
With HTTP POST/PUT also we can send data to another application.
So how are two different at conceptual level?
They are the same thing. A webhook is a callback or event listener concept for the web that is implemented as an HTTP PUT or POST. It could be implemented as a GET if this information is small.
To make it work, you register your webhook address with someone else's server. It could be an address like https://yourcompany.com/notifyme. Then that other server will send an HTTP PUT or POST request to the address you registered when some event occurs.
I think this is confusing because the terms web and hook are so broad that they are almost meaningless. A hook is something a pirate replaces his missing hand with. The terms API callback or listener API would be much more intuitive.