Yeah it is a proxy. I feel that in general we always use the term proxy as short for transparent proxy, while "server" is a bit more general purpose.

If you squint hard enough you can call almost any server a proxy. An FTP server is a proxy for data on disk. Github.com is a proxy for a git repo.

But yeah, saying "MCP is a proxy to your application" might be more insightful than "MCP is a client to your application"

"server" implies that the content being served has the same owner/same scope of control and trust. the sysadmin of an ftp server is the one owning the disk that the ftp server uses; github.com controls the repos that are available on the github site.

i think this whole "mcp security is terribad" thing spawns from the incorrect categorization of the thing as a "server" - if it were instead called a proxy, the rabble would die down.