I see this expression a lot to explain seeming contradictions in puranas. kalpa-bheda could mean difference between kalpas - does that mean all puranic stories happen repeatedly from one kalpa to the next and that there may be variations in the narrative among different kalpas?
What does the expression “kalpa bheda” mean?
Kalpa Bheda means differences due to Kalpa or cycle (in Hinduism, a kalpa is equal to 4.32 billion years, a "day of Brahma" or one thousand chaturyugas).
Does that mean all puranic stories happen repeatedly from one kalpa to the next and that there may be variations in the narrative among different kalpas?
Not sure about all but most of the stories are repetitive and happen repeatedly from one kalpa to the next.
This is explained in this Chaupai of Ramcharitmanas 1.33:
कीन्हि प्रस्न जेहि भाँति भवानी। जेहि बिधि संकर कहा बखानी।।
सो सब हेतु कहब मैं गाई। कथाप्रबंध बिचित्र बनाई।।
जेहि यह कथा सुनी नहिं होई। जनि आचरजु करैं सुनि सोई।।
कथा अलौकिक सुनहिं जे ग्यानी। नहिं आचरजु करहिं अस जानी।।
रामकथा कै मिति जग नाहीं। असि प्रतीति तिन्ह के मन माहीं।।
नाना भाँति राम अवतारा। रामायन सत कोटि अपारा।।
कलपभेद हरिचरित सुहाए। भाँति अनेक मुनीसन्ह गाए।।
करिअ न संसय अस उर आनी। सुनिअ कथा सारद रति मानी।।
I shall now relate at some length the seed of the story-viz., how Goddess Bhavåni (Pårvati) questioned Lord Sankara and how the latter answered Her questions - weaving a strange narrative round this episode.
Let no one who should happen not to have heard this anecdote before be surprised to hear it.
Wise men who hear this uncommon, legend marvel not; for they know there is no limit to the stories of Lord Råma in this world.
They are convinced in their heart that Lord Råma has bodied Himself forth in diverse ways and that the Råmåyana, though consisting of a thousand million verses, is yet infinite. Great sages have diversely sung the charming stories of Lord Hari, relating as they do to different Kalpas or cycles.
Bearing this in mind the reader should not entertain any doubt and should hear this narrative reverently and with devotion.
राम अनंत अनंत गुन अमित कथा बिस्तार।
सुनि आचरजु न मानिहहिं जिन्ह कें बिमल बिचार।।33।।
Råma is infinite, infinite are His virtues and the dimensions of His story are also immeasurable. Those whose thoughts are pure will, therefore, feel no surprise when they hear it.
Ramcharitmanas 1.122 - 1.76 gives brief account of Ramaavtara of few diff Kalpas:
- In one kalpa, Vishnu's dwarpala Jaya and Vijay were cursed by Sanat Kumaras and incarnated as Hiranyakashipu and Hiranyaksha and they further incarnated as Ravana and Kumbhakarana:
द्वारपाल हरि के प्रिय दोऊ। जय अरु बिजय जान सब कोऊ।। बिप्र श्राप तें दूनउ भाई। तामस असुर देह तिन्ह पाई।। कनककसिपु अरु हाटक लोचन। जगत बिदित सुरपति मद मोचन।। ...
मुकुत न भए हते भगवाना। तीनि जनम द्विज बचन प्रवाना।। एक बार तिन्ह के हित लागी। धरेउ सरीर भगत अनुरागी।। कस्यप अदिति तहाँ पितु माता। दसरथ कौसल्या बिख्याता।। एक कलप एहि बिधि अवतारा। चरित्र पवित्र किए संसारा।।
- In one kalpa, Jalandhar's wife Vrinda curses Vishnu, Jalandhar incarnated as Ravana:
एक कलप सुर देखि दुखारे। समर जलंधर सन सब हारे।। ... तहाँ जलंधर रावन भयऊ। रन हति राम परम पद दयऊ।। एक जनम कर कारन एहा। जेहि लागि राम धरी नरदेहा।।
- In one kalpa, Narada curses Vishnu, Shiva's ganas incarnated as Ravana and Kumbhakarana:
नारद श्राप दीन्ह एक बारा। कलप एक तेहि लगि अवतारा।। ... हर गन हम न बिप्र मुनिराया। बड़ अपराध कीन्ह फल पाया।। श्राप अनुग्रह करहु कृपाला। बोले नारद दीनदयाला।। निसिचर जाइ होहु तुम्ह दोऊ। बैभव बिपुल तेज बल होऊ।। भुजबल बिस्व जितब तुम्ह जहिआ। धरिहहिं बिष्नु मनुज तनु तहिआ।
- In one kalpa, king Pratapbhanu became Ravana and his brother Arimardan became Kumbhkarana:
काल पाइ मुनि सुनु सोइ राजा। भयउ निसाचर सहित समाजा।। दस सिर ताहि बीस भुजदंडा। रावन नाम बीर बरिबंडा।। भूप अनुज अरिमर्दन नामा। भयउ सो कुंभकरन बलधामा।।
This is also explained in Shiva Purana: RUDRASAMHITA: KUMARAKHANDA: Chapter 13. Birth of Ganesha
- Due to the difference of Kalpas, the story of the birth of GaneSa is told in different ways. According to one account he is born of the great lord. His head looked at by Sani was cut off and an elephant’s head was put on him.
- Now we narrate the story of the birth of GaneSa in Svetakalpa when his head was cut off by the merciful Siva.
IN an article by Swami B.V.Giri of Sri Narasingha Chaitanya Ashram titled The Supremacy of Srimad Bhagavatam over the Vedas he states "After Srila Vyasadeva divided the Vedas into four books (Rg, Yajur, Sama and Atharva), his disciples further divided them into 1,130 divisions. This is stated in the Kurma Purana (52.19-20):
eka-vimsati-bhedena rg-vedam krtavan pura
sakhanam satenaiva yajur-vedam athakarot
sama-vedam sahasrena sakhanam prabibheda sah
atharvanam atho vedam bibedha navakena tu
‘Previously the Rg Veda was divided into 21 sections, the Yajur Veda into 100 sections, the Sama Veda into 1,000 sections and the Atharva Veda into 9 divisions.’
Each division has 4 minor divisions, namely the Samhitas, Brahmanas, Aranyakas and Upanisads. Thus altogether the 4 Vedas contain 1,130 Samhitas, 1,130 Brahmanas, 1,130 Aranyakas, and 1,130 Upanisads. This makes a total of 4,520 divisions.
At present, most of these texts have disappeared due to the influence of time. We can only find 11 Samhitas, 18 Brahmanas, 7 Aranyakas and 220 Upanisads which constitutes a mere 6% of the entire Vedic canon!"
Therefore, our knowledge of God derived from various Itihaasa Puranas are severely restricted. And we find anomalies in various scriptures.
For instance, probably the most famous story - 'How Ganesha got the Elephant Head'. the more popular version, probably from Shiva Purana (I'm not very certain, but this tale is told in Wikipedia):
Goddess Parvati had started preparing for a bath. As she didn’t want to be disturbed during her bath and she had no gana of her own, Goddess Parvati took the turmeric paste (for bathing) from her body and made a form of a boy and breathed life into him. This boy was instructed by Goddess Parvati to guard the door and to not let anyone in till she finished her bath.
Lord Shiva wanted to go and see Parvati but found himself being stopped by this strange boy. Shiva tried to reason with the boy saying that he was Parvati's husband but the boy did not listen and was determined to not let Shiva enter till his mother Goddess Parvati finished her bath. The boy's behaviour surprised Shiva. Sensing that this was no ordinary boy, Shiva severed the boy's head with his Trishul thereby killing him instantly.
When Parvati learned of this, she was so enraged and insulted that she decided to destroy the entire Creation. At her call, she summoned all of her ferocious multi-armed forms, the Yoginis arose from her body and threatened to destroy all. She said she would re-consider her plan, but only if two conditions were met: one, that the boy be brought back to life, and two, that he be forever worshipped before all the other gods.
Shiva, having cooled down by this time, agreed to Parvati’s conditions. He sent his Shiva-dutas out with orders to bring back the head of the first creature that is lying dead with its head facing North. The Shiva-dutas soon returned with the head of a strong and powerful elephant Gajasura which Lord Brahma placed onto boy's body. Breathing new life into him, he was declared as Gajanana and gave him the status of being foremost among the gods, and leader of all the ganas (classes of beings), Ganapati.
Brahma Vaivarta Purana narrates a different version:
Parvati fasted for a year (punyaka vrata) to propitiate Vishnu so that he would grant her a son. Vishnu, after the completion of the sacrifice, announced that he would incarnate himself as her son in every kalpa. Accordingly, Ganesha was born to Parvati as a charming infant. This event was celebrated with great enthusiasm and all the gods were invited to take a look at the baby. However Shani (Saturn), the son of Surya, hesitated to look at the baby since Shani was cursed with the gaze of destruction. However Parvati insisted that he look at the baby, which Shani did, and immediately the infant's head fell off. Seeing this, Vishnu mounted on Garuda and rushed to the banks of the Pushpa-Bhadra river, from where he brought back the head of a young elephant. The head of the elephant was joined with the headless body of Parvati's son, thus reviving him. The infant was named Ganesha and all the Gods blessed Ganesha and wished Him power and prosperity.
Two versions and both from our eighteen Puranas - which is correct and or acceptable. And both versions have their followers, who insist their's is the correct version. There are many similar episodes in our Itihaasa Puranas. How to clarify / justify such anomalies - the events occurred in different Kalpas, hence Kalpa Bheda.
As per Sanatana dharma, the cycle of Cosmic Creation and Destruction goes on ceaselessly, hence events and occurrence are repeated in each cycle. This probably is the genesis of the term Kalpa Dheda.