docs: say out loud that mcp.run() is a stdio server, on the host page

"Connect to a real host" showed a server file ending in mcp.run() and
never said what that call does, which is the one fact the whole page
stands on: with no arguments it is a STDIO server -- it blocks, reads
protocol messages on stdin, writes them on stdout, and never opens a
port. That is why every host on the page is configured with a command
rather than an address. Running your server explains this, but a
reader lands on this page from the Get started sequence (or a search)
without having read that one.

The same page now also answers the two questions a reader has next, in
one note: this is the LOCAL story (to serve people who don't have your
file, you hand out a URL -- Running your server, then Deploy & scale),
and a host is just an application with an MCP client inside, so your
own Python can play that part (Client transports launches the same
file with stdio_client). Client transports points back the other way.

Author: maxisbey

docs/client/transports.md

@@ -72,7 +72,7 @@ Two things to notice:
 
 ## stdio
 
-A **stdio** server is a subprocess. The client launches it, writes JSON-RPC to its stdin and reads JSON-RPC from its stdout. It is how a desktop host runs a server on your machine.
+A **stdio** server is a subprocess. The client launches it, writes JSON-RPC to its stdin and reads JSON-RPC from its stdout. It is how a desktop host runs a server on your machine — a host *is* this code plus a UI, and **[Connect to a real host](../get-started/real-host.md)** is the same relationship seen from the host's side, as a config file.
 
 Describe the process with `StdioServerParameters`, turn it into a transport with `stdio_client`, and hand *that* to `Client`:
 

docs/get-started/real-host.md

@@ -10,8 +10,9 @@ Which means connecting to a host is one act: you tell it **the command that star
 --8<-- "docs_src/real_host/tutorial001.py"
 ```
 
-Two tools and a resource, one file. Two things about that file matter to every host below:
+Two tools and a resource, one file. Three things about that file matter to every host below:
 
+* `mcp.run()` with no arguments starts a **stdio** server: it blocks, reads protocol messages on stdin, and writes them on stdout. That is the transport every host on this page speaks — the host starts your file as a child process and owns those two pipes — and it is why connecting is only ever "here is the command". You never pick a port, and nothing listens on one.
 * `run()` is under `if __name__ == "__main__":`. Everything below **imports** this file rather than executing it, so an unguarded `run()` would start a server the moment anything loaded the module.
 * The server object is a module-level global named `mcp`. That's the name `mcp run` looks for (`server` and `app` also work). Call it something else and you name it explicitly: `mcp run server.py:bookshop`.
 
@@ -39,6 +40,19 @@ It is also the command `mcp install` writes into Claude Desktop's config for you
     `uv` with the absolute path from `which uv` (macOS/Linux) or `where uv` (Windows). That is
     exactly what `mcp install` writes.
 
+!!! note "This page is the local story"
+    Everything here runs your server on the machine the host is on: the host launches your
+    file, over stdio. That is exactly right for a personal or single-machine tool. To give a
+    server to people who do *not* have your file, you hand out a **URL**, not a command — the
+    same `mcp` object served over Streamable HTTP. **[Running your server](../run/index.md)**
+    is that decision in one table, and **[Deploy & scale](../run/deploy.md)** is the road from
+    there to a real hostname.
+
+    And a host is nothing more than an application with an MCP client inside it, so your own
+    Python can play the host's part: **[Client transports](../client/transports.md)** launches
+    this same file as a subprocess with `stdio_client(...)`, and **[Testing](testing.md)**
+    connects to it in memory with no process at all.
+
 ## Claude Desktop
 
 The one host the SDK can configure for you: