The definition of Singleton is: a class ensuring that there is only one instance of it and providing a global point of access to it by a class method.
What you presented are just the two most typical implementations.
The one assigning the instance at the field declaration has the advantage that it is inherently thread-safe.
The other, using lazy initialization, needs some amount of explicite synchronization, but defers the creation of the instance until you really need it for the first time.
Did that help?
PS: Singleton is one of the simplest design
patterns, but also one of the easiest to be misused. Be *very* wary at applying it!
See also
http://c2.com/cgi/wiki?SingletonPattern
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