How to use lithium-ion batteries and precautions for charge/discharge circuits

Very confusing.

I feel like explaining this youtube

Can a charging board and a lithium-ion battery with protection circuit be used together?

Introduction to Design Methods for Power Supply Circuits for Portable Devices

When charging from an external source, the supply from the battery to the circuit is cut off using a changeover switch!

However, the aitendo board below does not seem to do so,

This is the charging circuit only.

This is the charging circuit + protection

There are also two types of lithium-ion batteries

Battery only, battery + protection