WSAPI is an API that abstracts the web server from Lua web applications from the web server, and a module that implements this API for CGI, FastCGI and Xavante, on UNIX and Windows. (Mod_Wombat implementation is in the works.) The WSAPI module also provides the application with basic web functionality (dealing with cookies, headers, etc.)
Sputnik implements a "WSAPI app" and can be called by any client that presents the same (really simple) API as WSAPI.
At the moment, Sputnik also works with CGILua. It does so by using a fairly simple wrapper that makes CGILua look like a WSAPI server.