docs: Clarify server-client relationship (modelcontextprotocol#1631)

* docs: Clarify server-client relationship

* fix: Linting error

* chore: Addres review feedback

* Update docs/docs/learn/architecture.mdx

Co-authored-by: Cliff Hall <[email protected]>

* Update docs/docs/learn/architecture.mdx

Co-authored-by: Cliff Hall <[email protected]>

* chore: Fix linting issue

* Update docs/docs/learn/architecture.mdx

Co-authored-by: Jonathan Hefner <[email protected]>

* Update docs/docs/learn/architecture.mdx

Co-authored-by: Jonathan Hefner <[email protected]>

* Update transport documentation to clarify stdio one-to-one relationship

- Remove transport-specific clarification from 2024-11-05 specification
- Add stdio transport clarification to draft specification
- Aligns with architecture documentation updates

* further architecture doc fixes

* some further changes to architecture doc

* Update architecture.mdx documentation

* chore: omitted suggested doc change in transports.mdx

---------

Co-authored-by: sdmcraft <[email protected]>
Co-authored-by: Cliff Hall <[email protected]>
Co-authored-by: Satya Deep Maheshwari <[email protected]>
Co-authored-by: Jonathan Hefner <[email protected]>

Author: 4 people

docs/docs/learn/architecture.mdx

@@ -28,7 +28,9 @@ The Model Context Protocol includes the following projects:
 
 ### Participants
 
-MCP follows a client-server architecture where an MCP host — an AI application like [Claude Code](https://www.anthropic.com/claude-code) or [Claude Desktop](https://www.claude.ai/download) — establishes connections to one or more MCP servers. The MCP host accomplishes this by creating one MCP client for each MCP server. Each MCP client maintains a dedicated one-to-one connection with its corresponding MCP server.
+MCP follows a client-server architecture where an MCP host — an AI application like [Claude Code](https://www.anthropic.com/claude-code) or [Claude Desktop](https://www.claude.ai/download) — establishes connections to one or more MCP servers. The MCP host accomplishes this by creating one MCP client for each MCP server. Each MCP client maintains a dedicated connection with its corresponding MCP server.
+
+Local MCP servers that use the STDIO transport typically serve a single MCP client, whereas remote MCP servers that use the Streamable HTTP transport will typically serve many MCP clients.
 
 The key participants in the MCP architecture are:
 
@@ -37,24 +39,25 @@ The key participants in the MCP architecture are:
 - **MCP Server**: A program that provides context to MCP clients
 
 **For example**: Visual Studio Code acts as an MCP host. When Visual Studio Code establishes a connection to an MCP server, such as the [Sentry MCP server](https://docs.sentry.io/product/sentry-mcp/), the Visual Studio Code runtime instantiates an MCP client object that maintains the connection to the Sentry MCP server.
-When Visual Studio Code subsequently connects to another MCP server, such as the [local filesystem server](https://github.com/modelcontextprotocol/servers/tree/main/src/filesystem), the Visual Studio Code runtime instantiates an additional MCP client object to maintain this connection, hence maintaining a one-to-one
-relationship of MCP clients to MCP servers.
+When Visual Studio Code subsequently connects to another MCP server, such as the [local filesystem server](https://github.com/modelcontextprotocol/servers/tree/main/src/filesystem), the Visual Studio Code runtime instantiates an additional MCP client object to maintain this connection.
 
 ```mermaid
 graph TB
     subgraph "MCP Host (AI Application)"
         Client1["MCP Client 1"]
         Client2["MCP Client 2"]
         Client3["MCP Client 3"]
+        Client4["MCP Client 4"]
     end
 
-    Server1["MCP Server 1<br/>(e.g., Sentry)"]
-    Server2["MCP Server 2<br/>(e.g., Filesystem)"]
-    Server3["MCP Server 3<br/>(e.g., Database)"]
+    ServerA["MCP Server A - Local<br/>(e.g. Filesystem)"]
+    ServerB["MCP Server B - Local<br/>(e.g. Database)"]
+    ServerC["MCP Server C - Remote<br/>(e.g. Sentry)"]
 
-    Client1 ---|"One-to-one<br/>connection"| Server1
-    Client2 ---|"One-to-one<br/>connection"| Server2
-    Client3 ---|"One-to-one<br/>connection"| Server3
+    Client1 ---|"Dedicated<br/>connection"| ServerA
+    Client2 ---|"Dedicated<br/>connection"| ServerB
+    Client3 ---|"Dedicated<br/>connection"| ServerC
+    Client4 ---|"Dedicated<br/>connection"| ServerC
 ```
 
 Note that **MCP server** refers to the program that serves context data, regardless of