What Is The Difference Between Webcasting And Podcasting ?

Webcasting is streaming of a live or taped event. You'll need an open and constant connection to the internet to hear and/or watch the whole thing. Once you finish watching and/or listening to the webcast you no longer have access to it as it isn't stored directly on your computer or device. You will have to stream the video and/or audio webcast again if you happen to have an internet connection.
http://en.wikipedia.org/wiki/Webcast

Podcasting involves downloading an already completed event in a singular file. Once you have the file loaded on your computer or device, you no longer need an internet connection to listen and/or watch the podcast as the file has been saved to your computer or device.
https://en.wikipedia.org/wiki/Podcast

I think Webcasts and Podcasts are two different methods of distributing content to a large number of recipients by the Internet.
A webcast is a live transition of media over a network like: Live classroom lectures, radio transition etc.
A Podcast is transmission of recorded media from one system to another system like: downloading mp3 from your PC to your mobile for later listening.