Singleton's in Mutliple Programs

Question

My basic question is, if in my program I create a singleton class, but I run my program multiple times, do the the programs share the same class, or each make their own? I ask because I feel like I've seen both behavior, but can't tell what the difference was. Heres what I saw:
1. I wrote a class which uses com.sun.tools.javadoc.Main.execute() to read javadoc info and relay it back to my program. The class called SmartDoclet was a singleton class, as well as a Doclet. So I would call execute() giving SmartDoclet in as the custom Doclet class, javadoc would run my class, which would then communicate back to my "main" program via the singleton object and pass the RootDoc object which was created. Worked perfectly, which makes me think singleton's are shared across all programs.
2. But at the same time, I've written GUI programs where the top-level JFrame was a singleton so that I had easy access to common commands, reading properties, etc... and I've tried running multiple instances of the program and it works fine (i.e. multiple JFrame's).
So I guess what I dont understand is whats the difference between these two scenarios. What makes #1 not "step out" of the program, like just running the same program from the command line twice would do. Any help appreciated!

Answer 1

Is the danger that someone might make the Singleton
cloneable really a the most important reason to make a
Singleton non-extensible? I think not.It IS a good reason if cloning or subclassing it means
you can end up with more than one in the same JVM. If
you really implemented Singleton because "There Can
Only BE One", I'd say prohibiting subclassing and
cloning might be important.
I gotta go with the OP on this. That comment is abit queer.
I gotta go with the definition of Singleton on this
and disagree. It's not like it's that difficult.
Don't implement Cloneable or Serializable and make
the constructors private. Done. What's the
problem?
At some point it is just too much.
Are you going to implement a security manager as well? Because unless you do I can create JNI method and create a new object as well.
If they don't understand that the singleton is a singleton then are you going to assume that that is the only problem that they are having?
When I program I make assumptions about those that I work with and those that will come after me. I like to think that they have a minimal level of intelligent. They might not write the best code all the time but they do understand most of the ideas. And given that singleton the most used and probably easiest pattern to understand is it really necessary to be so protective?