Java JDK or JRE or both are specifications? Can anyone quote some relevant implementations?
The JDK (Java Developer Kit) and JRE (Java Runtime Environment) are (in part) both implementations of the Java Language Specification and The Java Virtual Machine Specification. JRE and JDK may or may not refer to the Sun JRE and Sun JDK depending on context. You can see this list of JVMs (Java Virtual Machines). There are also third-party java compilers, the most popular being ecj and gcj.
JDK is Java Development Kit, a toolset used to write Java programs. JRE is Java Runtime Environment, the virtual machine that executes Java bytecode. Naturally the Sun implementations of both are widely used
JRE definition from java.com:
The Java Runtime Environment (JRE) is what you get when you download Java software. The JRE consists of the Java Virtual Machine (JVM), Java platform core classes, and supporting Java platform libraries. The JRE is the runtime portion of Java software, which is all you need to run it in your Web browser.
And here is an article from wikipedia about what is JDK