iterator is a more general concept: any object whose class has a next method (__next__ in Python 3) and an __iter__ method that does return self.
Every generator is an iterator, but not vice versa. A generator is built by calling a function that has one or more yield expressions (yield statements, in Python 2.5 and earlier), and is an object that meets the previous paragraph's definition of an iterator.
You may want to use a custom iterator, rather than a generator, when you need a class with somewhat complex state-maintaining behavior, or want to expose other methods besides next (and __iter__ and __init__). Most often, a generator (sometimes, for sufficiently simple needs, a generator expression) is sufficient, and it's simpler to code because state maintenance (within reasonable limits) is basically "done for you" by the frame getting suspended and resumed.
For example, a generator such as:
def squares(start, stop):
for i in range(start, stop):
yield i * i
generator = squares(a, b)
or the equivalent generator expression (genexp)
generator = (i*i for i in range(a, b))
would take more code to build as a custom iterator:
class Squares(object):
def __init__(self, start, stop):
self.start = start
self.stop = stop
def __iter__(self): return self
def next(self):
if self.start >= self.stop:
raise StopIteration
current = self.start * self.start
self.start += 1
return current
iterator = Squares(a, b)
