epoch vs. iteration in recurrent neural networks

I am looking at the text generation example of Keras using RNN and LSTM but still confused about the difference between the terms epoch and iteration.

Even though, here is a previous question asking the same thing, I cannot understand the answer, or this answer is different from how I understand it and also different from how the following example handles it. Based on this answer, it is said that

one epoch = one forward pass and one backward pass of all the training examples

number of iterations = number of passes, each pass using [batch size] number of examples.

Example: if you have 1000 training examples, and your batch size is 500, then it will take 2 iterations to complete 1 epoch.

Conclude this: (#training examples/batch size) = (#iterations/#epochs).

However, the following example, as I understand, is different from the previous conclusion.

# train the model, output generated text after each iteration
for iteration in range(1, 60):
    print()
    print('-' * 50)
    print('Iteration', iteration)
    model.fit(X, y, batch_size=128, nb_epoch=1)

    start_index = random.randint(0, len(text) - maxlen - 1)

    for diversity in [0.2, 0.5, 1.0, 1.2]:
        print()
        print('----- diversity:', diversity)

        generated = ''
        sentence = text[start_index: start_index + maxlen]
        generated += sentence
        print('----- Generating with seed: "' + sentence + '"')
        sys.stdout.write(generated)

        for i in range(400):
            x = np.zeros((1, maxlen, len(chars)))
            for t, char in enumerate(sentence):
                x[0, t, char_indices[char]] = 1.

            preds = model.predict(x, verbose=0)[0]
            next_index = sample(preds, diversity)
            next_char = indices_char[next_index]

            generated += next_char
            sentence = sentence[1:] + next_char

            sys.stdout.write(next_char)
            sys.stdout.flush()
        print()

Here, the iteration is 60 and number of epoch is set to 1, which confused me a lot. It seems like, there are 60 iterations, as stated for iteration in range(1, 60). And for each of the iteration, one epoch was done as stated model.fit(X, y, batch_size=128, nb_epoch=1) for each for-loop. And again, here, there is a batch_size=128. So what does the iteration exactly mean?

Anyone can explain the difference between iteration and epoch based on this example?