I want to know the differences / similarities between Hibernate and simple persistence in Java EE 5?
Standardized Java API EE 5 retention is JPA 1.0 and is a kind of unified version of the API and EJB 2 CMP, JDO, Hibernate, and TopLink products. Hibernate is an ORM structure that precedes JPA and has greatly influenced the JPA specification (the creator of Hibernate is part of an expert group behind JPA). Just keep in mind that JPA is just an API, you need a JPA implementation to use it.
I don’t understand if Hibernate implements a Java EE 5 persistence implementation or if this is a completely different approach to representing data on internal systems.
Yes, Hibernate provides a JPA implementation (and also extends it; Hibernate is a superset of JPA) through the Hibernate EntityManager project (which relies on Hibernate Core).
I am confused by Hibernate and its relation to the concepts of Java security provided in the Java EE 5 tutorial ... Can you clarify the role of Hibernate in the context of Entities and EJB?
Hibernate can be used as a provider for preserving JPA duration, i.e. as part of the code that actually stores EJB 3 objects (the JPA specification was part of the EJB 3.0 specification in version 1.0, now it's a separate specification)
Also, I want to know other approaches (frameworks) like JPA or Spring ...
Spring is not the foundation of conservation, Spring is an IoC container, it does not compete with Hibernate.
Hibernate's corresponding JPA alternatives include TopLink Essentials (RI in Java EE 5), EclipseLink (which is also RI JPA 2.0 in Java EE 6), OpenJPA, DataNucleus.
Other save options are JDO (another standardized save API), iBATIS (not ORM, it's more like data mapping), JDBC (low level API) to reference the most famous.
Check out this previous answer for a review and some historical background.