A Semi-Dedicated server CAN be a VPS setup, but certainly is not always the case.
I dont know why the previous poster thinks its a VPS; as in most cases its not, but the service may differ from provider to provider.
I like to think of a Semi-Dedicated as a shared-hosting server with just a few clients on it, hence giving you more processing power as a common shared-hosting server and often equal or (in some cases) larger resources available as a VPS.
A major difference between a VPS and a Semi-Dedicated is that a Semi-Dedicated gives you less freedom in installing whatever you want; while on the other hand gives you a full pro-active managed service (like on a shared hosting account).
I would say that a VPS and Semi-Dedicated are (looking at power) at equal positions in the market segment.
So a common upgrade strategy could be : Shared hosting -> Semi-Dedicated OR VPS -> Dedicated Servers