When you need to annotate a word or a phrase, you'll use Tags to say what the annotation is. Examples of tags are Person,Location,Object, Noun etc. You can use any tags in any language.
Classes are used when you want to annotate an entire example, as opposed to a word or phrase. Examples of classes might be Positive and Negative for sentiment, or Funny, Sad, Exciting for text classification.
You can define as many of your own classes as you want.
Single and Multi Class Classification
When you define your schema you can choose whether it is a single or multi class schema.
Use single class schemas when the classes are mutually exclusive. For example in sentiment analysis, a document can be positive or negative but not both. There is only one single answer.
Use multi class schemas when there can be more than one correct class. For example a document can be both funny and sad, a support inquiry may be about both billing and technical issues.