Singleton Class :
Singleton Class is class of which only single instance can exists per classloader.
Helper Class (Class with only static fields/methods) :
No instance of this class exists. Only fields and methods can be directly accessed as constants or helper methods.
These few lines from this blog describes it nicely:
Firstly the Singleton pattern is very
useful if you want to create one
instance of a class. For my helper
class we don't really want to
instantiate any copy's of the class.
The reason why you shouldn't use a
Singleton class is because for this
helper class we don't use any
variables. The singleton class would
be useful if it contained a set of
variables that we wanted only one set
of and the methods used those
variables but in our helper class we
don't use any variables apart from the
ones passed in (which we make final).
For this reason I don't believe we
want a singleton Instance because we
do not want any variables and we don't
want anyone instantianting this class.
So if you don't want anyone
instantiating the class, which is
normally if you have some kind of
helper/utils class then I use the what
I call the static class, a class with
a private constructor and only
consists of Static methods without any
any variables.