Good questions. The Jupyter server is running on the PYNQ-Z2 board, and serves the data in the Jupyter notebook in your web browser in your host PC. The web browser on your PC is your interface to the board.
Python and PYNQ code in a notebook runs on the board.
However, the Notebook is rendered by your host PC. This means that if, for example, you process some data on your PYNQ-Z1 and plot it in a graph in a notebook, your CPU plots the graph.
If your graph takes a lot of time to render, you may notice different performance on different host PCs.