Update debugging.mdx

Author: jspahrsummers

docs/tools/debugging.mdx

@@ -129,7 +129,7 @@ When servers fail to connect:
 
 ### Server-side logging
 
-When building a server that uses the local stdio [transport](/docs/concepts/transports), all messages logged to stderr (standard error) will be captured by the client (e.g., Claude Desktop) automatically.
+When building a server that uses the local stdio [transport](/docs/concepts/transports), all messages logged to stderr (standard error) will be captured by the host application (e.g., Claude Desktop) automatically.
 
 <Warning>
   Local MCP servers should not log messages to stdout (standard out), as this will interfere with protocol operation.