Server.Transfer is page processing form one page directly to nex page with out making any round trips back to cleints browser.it doesn't update the client url history.its safe through network.

Response.Redirect is redirects page to another browser or site.

Yes,server.Transfer isexecutes the form within the page,its not go to other page,but Response.redirect is executes the form into other page.

when user does not want to change the address of the url.Then server.transfer is very useful for existing in same url address with opening different forms . Means it proves the transfer of form in rond trip back to clients browser. It is very helpful for security purpose.
Server.Transfer is page processing form one page directly to nex page with out making any round trips back to cleints browser.
Response.Redirect is redirects page to another browser or site.