I know that classes are objects in C#, and can be used in various ways.
Class is not an object. Class is a model to be followed, object uses this model to structure.
Think about development time and runtime. Class is defined in the first, the object in the second. Class only exists in your code, object only exists when the application is running. It is a simplification, but so it is easy to understand.
Comparing to database, the structure defined for a table is the class, each row of this table is the object.
Would the class itself be considered an entity of the system or not? If so, I believe that the above sentence would have to be different.
Yes, a class is an entity model of the system. I don’t see why it should be different. From an architectural point of view, the class is a model representing an entity. Architecture only exists on paper, its realization will generate objects. Objects function as entities. Example: the class tells how a client’s data should be organized, but a client will only exist in fact on objects.
Just as tables in Dbs are entities, classes are entities in the modeling. Separate the real data model from your mind.
Just be careful because in programming languages mainstream where it reads attribute, understand as fields, or even properties, since the term is used for something else.
When we speak of entities, we can refer only to the class or to any object?
The entity itself is the object. The class is a type of an entity, or in other words, it is an object class. Class comes from classification, comes from generalization of a group of objects with the same characteristics. Class is an abstraction of the entity. When we’re talking about abstraction, we use the term entity, but actually that’s a kind of entity.
Think of a map. We point to such a city. We are pointing to an abstraction that represents the city on that screen, but it is not the city. The city is an entity. On the map we treat that representation as if it were an entity. The term can be used in both contexts, but the most correct would be to say "representation of the city on the map". The important thing is that if you only speak "city" on a map everyone understands that it is only one representation.
A philosophical note
Technically the object of the application is also not the entity, we just use the term so to facilitate. The same entity exists only in the real world. So a customer is the same customer, is a person or a company. The object in your application works as a representative figure. For your application the real world does not exist. Tron exists only in fiction.
You saw it in some book, on the web there’s nothing like it.
– Maniero