If by web server you mean physical computer, absolutely they could be on different servers. Google and Akamai, among others, have large collections of machines serving the same domain names. It helps with speed, since you are likely to receive pages from a server near you.
In general, it does not appear to be possible to reliably tell whether you are talking to the exact same server before and after a redirect. First, it is difficult to test for IP addresses from a Web page (see, e.g., this question and this one). Second, even if the IP addresses are the same before and after the redirect, they may be on different machines. For example, TCP anycast can change which server you are talking to without changing the IP address. Also, network address translation and load-balancing may change which server you are talking to behind a firewall, which you would probably have no way of finding out unless the server provided some ID of its own.