From the web server's point of view, both are identical TCP/IP connections, just coming from different locations. The server cannot see which route the packets traveled, and doesn't automagically know that there's a VPN server running at a certain address.
However, a server can be configured to, for example, only allow (or deny) connections from certain addresses. If the VPN is a public service, then its IP address blocks are often listed somewhere, and might be blocked by some administrators (depending on the service's popularity and/or abuse record). The opposite is also possible – some VPN services explicitly deny access to certain web sites.
Finally, since the VPN server is at a different location than you are, it is possible that there are network problems somewhere between web and VPN servers, that just have gone unnoticed because nobody complained.