What is the difference between Work and The Internet in the connection settings?

The Internet setting is really designed for a direct connection to a service such as you have with a dial-up or when using a proxy server. Work would more properly be called network but relates back a few years when many people had networks in their work place, but only a dialup connection at home. Usually either setting will work on hotspots but if you want to use your home network for more than web access, "work" is the setting that usually works best.