But, like pancakes, usually the stack is described as building bottom-up. Can you relate the individual components to ingredients in a diner-style pancake breakfast?

Bottom line is that MCP doesn't change anything in the way the model discovers and invokes tools, so MCP doesn't help with the issue of lack of standard tool call syntax.

1) The way basic non-MCP tool use works is that the client (e.g. agent) registers (advertises) the tools it wants to make available to the model by sending an appropriate chunk of JSON to the model as part of every request (since the model is stateless), and if the model wants to use the tool then it'll generate a corresponding tool call chunk of JSON in the output.

2) For built-in tools like web_search the actual implementation of the tool will be done server-side before the response is sent back to the client. The server sees the tool invocation JSON in the response, calls the tool and replaces the tool call JSON with the tool output before sending the updated response back to the client.

3) For non-built-in tools such as the edit tool provided by a coding agent, the tool invocation JSON will not be intercepted server-side, and is instead just returned as-is to the client (agent) as part of the response. The client now has the responsibility of recognizing these tool invocations and replacing the invocation JSON with the tool output the same as the server would have done for built-in tools. The actual "tool call" can be implemented by the client however it likes - either internal to the client to by calling some external API.

4) MCP tools work exactly the same as other client-provided tools, aside from how the client learns about them, and implements them if the model chooses to use them. This all happens client side, with the server/model unaware that these client tools are different from any others it is offering. The same JSON tool registration and JSON tool call syntax will be used.

What happens is that client configuration tells it what MCP servers to support, and as part of client initialization the client calls each MCP server to ask what tools it is providing. The client then advertises/registers these MCP tools it has "discovered" to the model in the normal way. When the client receives a tool call in the model response and sees that it is an MCP provided tool, then it knows it has to make an MCP call to the MCP server to execute the tool call.

TL/DR

o the client/agent talks standard MCP protocol to the MCP servers

o the client/agent talks model-specific tool use protocol to the model