What's the difference between entity and class?

A class is a template for an object (among other things), and is a very general concept.

An entity has more semantic significance and is usually tied to a concept (possibly about a real object for example, an Employee or a Student or a Music Album) and is linked to business logic.

Entities are usually used to establish a mapping between an object and to a table in the database. Entities are also known as domain objects. Like I mentioned before, entities will be used in situations where there is business logic and as such it hold information about the system (or part of the system) that it is modeling.

To add one more point

Class is a syntactic i.e. A set or category of things having some property or attribute in common and differentiated from others by kind, type, or quality.

Entity is a semantic i.e. relating to meaning in language or logic. An entity is something that exists in itself, actually or potentially, concretely or abstractly, physically or not. It needs not be of material existence.

Object is a in-memory value referenced by identifier, it is an instance of a Class.