Actually, No both Ramayana and Mahabharata are from same Kalpa only but from different Manvantaras.
See, the following Kalpa chart.
The fact is, despite there being 71 cycles of four yugas in each manvantara oir current manvantara is Vaivasvata Manvantara, yet we cannot say that in every dwapara yuga Krishna comes, in every treat yuga Rama comes and so on. The truth is – Vishnu’s dasavataras span the entire manvantara; and they do not ever repeat within the same manvantara. We are in 28th Dwapara-yuga and the Rama incarnation happened in 24th Treta yuga (i.e., in four chatur-yugas before, which is a very distant past). This is clearly evident from Harivamsa Parva as follows.
Harivamsha Parva of Mahabharata in chapter 41 describes the ten incarnations of Vishnu. There, although not all incarnations are specified in terms of yuga name; but most of them are said to be from ‘pura yuge’ (some past yuga). Only for Rama, Vyasa and Krishna the yuga names are recounted. However, these three itself are enough to understand that all the ten incarnations didn’t happen in the four consecutive yugas. All the ten incarnations span across the entire epoch. Between Rama and Krishna itself is a huge gap.
Rama incarnation happened in the twenty-fourth mahayuga’s treata yuga.
“caturviṃśe yuge cāpi viśvāmitra puraḥsaraḥ ।
rājño daśarathasya atha putraḥ padma-āyata-īkṣaṇaḥ ॥121
kṛtvā ātmānaṃ mahābāhuḥ caturdhā prabhuḥ īśvaraḥ ।
loke rāma iti khyātaḥ tejasā bhāskara-upamaḥ ॥“ (Harivamsha Parva 1:41:121-122)
“In kRita era belonging to the twenty-fourth mahA-yuga, the lotus-petal eyed viShNu, keeping sage vishvamitra as helmsman and making himself fourfold personalities, incarnated as the son of king dasha-ratha, where the other three personalities are bharata, lakshmana, and shatrughna, ramified as his brothers… and with a resplendence like that of the sun he that lord, controller, and ambidextrous viShNu is celebrated in this world by his name rAma”.
While Veda Vyasa as the son of satyavati incarnated in the dwapara yuga of the twenty-eighth maha yuga. This should be indicative for Krishna’s incarnation also as Vyasa who was satyavati’s son and Krishna appeared in the same dwapara yuga.
“navame dvāpare viṣṇuḥ aṣṭāviṃśe purā abhavat ।
vedavyāsaḥ tathā jajñe jātūkarṇya puraḥsaraḥ ॥161
eko vedaḥ caturdhā tu kṛtaḥ tena mahātmanā ।
janito bhārato vaṃśaḥ satyavatyāḥ sutena ca ॥“ (Harivamsha Parva 1:41:161-162)
“After the ninth incarnation of viShNu, the lord having sent beforehand sage jAtUkarna to study veda-s and purANA-s, took his birth as sage veda-vyAsa in the twenty-eighth dvApara era, to segregate one veda in four sections, and even to categorise purANA-s, for easy comprehensibility… This sage veda-vyAsa, engendered by lady satyavati, is the originator for the dynasty of bhAratA-s”.
The Puranas also describe Vishnu avatars that come during specific yugas, but may not occur in every Yuga Cycle.
Vamana appears at the beginning of Treta Yuga. According to Vayu Purana, Vamana's 3rd appearance was in the 7th Treta Yuga.
Rama appears at the end of Treta Yuga. According to Vayu Purana and Matsya Purana, Rama appeared in the 24th Yuga Cycle. According to Padma Purana, Rama also appeared in the 27th Yuga Cycle of the 6th (previous) manvantara.
This shows that in the entire manvantara there are no multiple Krishnas, multiple Ramas. Vishnu’s ten incarnations span entire manvantara.
Mahabharata is said to be the combination of all 18 puranas. So, it can stories about any kalpa. Even in Mahabharata itself there are instances where the story differs in different parvas. For example, the birth story of Skanda, etc. That's why the differences in the story.
There are 14 Manvantararas (Manus) in a Same Kalpa and each Manvantara has 71 Chatur Yugas in it. So, the differences in the stories.
There can also be a slight variations in the events with each Manvantara Bheda. But in Kalpa Bheda, the variations can be totally different sometimes. Like, each Puranas tells the story of different different Kalpas so the same story can sometime totally varies from puranas to puranas also.
"So, the Valmiki Ramayana and the VedaVyasa Mahabharata are from the same Kalpa only, even they are from same Manvantara, but from different Chatur Yugas."
I hope this clarifies your queries.