You can use the above links to read about each of these types of lists (including how to set them up) and determine which one meets your current needs.
In a nutshell though, Quicklists are dynamic groups of contacts pulled from your database based upon search criteria you have previously defined. If you anticipate one of your searches will be a common one, the use of Quicklists will allow you to keep updated results for a standing search query at your fingertips.
What distinguishes Tag Groups from QuickLists is that the process of adding contacts to or removing contacts from a Tag Group is manual. Contacts in your Tag Groups, in other words, are handpicked by you to be in that particular group.
In either case you'll most likely be using the Search functionality in Redtail to pull up your group of contacts for addition to one of these types of lists. You can learn more about Advanced Search within Redtail here.