Tags are like a digital post-it note. They provide ways to easily label contacts, such as "Prospect", "Customer", or "[Product Name]".
Groups are saved searches of your contacts. For example, you may want to know everyone who is a customer. You can then create a group with the criteria Contact Tag > Contains > Customer and it will search your whole database for people who have this tag, then save the search!
Check out ONTRAPORT's forum article on List Segmentation!