Both Server.Transfer and Response.Redirect methods are used to transfer a user from one web page to another web page. Both methods are used for the same purpose but still there are some differences as follows. Both method has same syntax like:
The difference between them is that the Response.Redirect method redirects a request to a new URL and specifies the new URL while the Server.Transfer method for the current request, terminates execution of the current page and starts execution of a new page using the specified URL path of the page.
Picked following summary from the link which Akshay has suggested
Redirection Redirection is done by the server. Redirection is done by the browser client.
Browser URL Does not change. Changes to the redirected target page.
When to use Redirect between pages of the same server. Redirect between pages on different server and domain.