Some more discussion on the confusion here https://github.com/modelcontextprotocol/modelcontextprotocol... where they acknowledge that most people call it a client and that that's ok unless the distinction is important.
I think host is a bad term for it though as it makes more intuitive sense for the host to host the server and the client to connect to it, especially for remote MCP servers which are probably going to become the default way of using them.