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Pyodide is a port of CPython to the WebAssembly platform. PyScript is a framework that uses Pyodide to provide a framework for developing Python applications in the browser. Its elevator pitch would be "python inside script tags via pyodide".

This uses pyodide. It's more like a Python to JS transpiler (even if it's not). It's to create browser apps using Python. So it's Pyodide + a browser API.

They also support MicroPython as an option now and not just Pyodide,

https://pyscript.net/tech-preview/micropython/about.html

In fact the main PyScript site uses MicroPython now, I see in the dev console (micropython.mjs and micropython.wasm).

Pyodide is a runtime.

PyScript can use Pyodide or MicroPython. MicroPython is actually quite small.

On top of the runtime, PyScript gives you some pleasantries and a lot of quality-of-life improvements for actually using Python for web programming, not just being able to run Python code.

Its a wrapper.