Is ‘Vayu Purāṇa’ a synonym for the Shiva Purāṇa and what is the reason for it having two names?

Question

The Matsya Purāṇa, while enlisting the 18 mahapuranas says the following with reference to the fourth one, also known as the Shri Shiva Purāṇa

With reference to the Śvetakalpa, the dharma which Vayu spoke (on this earth), the Purāṇa in which this (dharma) is compiled along with the greatness of Lord Shiva is known as the Vayaviya Purāṇa containing 24,000 verses. Whoever, in the month of Shravana on Purnima, donates this Purāṇa with jaggery a cow and a bull to the family priest, he shall reside in Shiva Loka for a kalpa.
-Matsya Purāṇa Chapter 53.18-19

The Matysa Purāṇa list doesn’t mention the words ‘Shiva Purāṇa’, yet the above emboldened words (Rudramahatmya, 24,000 verses, Shravana month, Shiva Loka) clearly refer to the Shiva Purāṇa, while calling it the Vayu Purāṇa. The note given by the publisher mentions a certain Shulapani attesting to the fact Vayu and Shiva are two names of the same Shiva Purana indeed:

When one has a look at the current Shiva Purana, among the 7 samhitas, there is one called Vayaviya Samhita, which clearly talks of Vayu teaching the sages about the details (or dharma) of Lord Shiva, an account of the Śveta Kalpa, in accordance with what the Matsya Purana states above.

Also to be noted that the Srimad Bhagavatam 12.7.23-24 makes no mention of a Vayu Purāṇa, and the fourth Purāṇa is correctly called by its original name, the Shiva Purāṇa.

However there is a separate Vayu Purana currently available too, but, except for a few chapters in the beginning and a few chapters scattered around (up till chapter 65), there is hardly any mention of anything related to Shiva. As usual, like the Puranas in circulation during the colonial and current era, there is overlap. The maximum corpus of the text of the Vayu Purāṇa is a direct copy paste version of the current Brahmanda Purāṇa, with the Gaya Mahatmya (dedicated to Bhagavan Vishnu) additionally at the end. As per the preface to this extant Vayu Purāṇa, it is primarily considered as Shiva Purana, but it gives due importance to the other two major deities, viz. Brahma (Brahmanda Purāṇa overlap) and Vishnu (Gaya Mahatmyam)

This very obvious overlap during the colonial era is a source of confusion as to the identity of the Vayu Purāṇa. A write-up while acknowledging the Vayu Purana to be related to Shaivism talks of this colonial era mishap:

However, the identity of this text, particularly from the Shiva Purana or Vayavya Purana, has long been a source of confusion since the 19th-century. Later scholarship has established that Vayu and Shiva Puranas are two different texts, but regionally only one of them was considered as a Maha-Purana.

We are therefore faced with a situation:

1. The Matsya Purāṇa (and Shulapani) is correct, and the extant Vayu Purāṇa is a clever colonial cook-up.
2. The Matsya Purāṇa is wrong which leads us to the question that in the list of 18, which Purāṇa is wrongly named therein leading to substitute the name ‘Vayu’ for the Shiva Purana i.e. which Purāṇa is to be struck off. Then what are the contents of the actual Vayu Purāṇa? If these are correct then what are the contents of the Brahmanda Purāṇa, and other such confusions.

Accordingly I ask:

Questions:

1. Is ‘Vayu Purāṇa’ a synonym for the Shiva Purāṇa, and the reason for a dual name. What does the orthodox Hindu tradition (shaivism or others) say in this regard. (most likely and obviously this is the actual case)
   
   Would like the view with proof (quoting verses) from traditional sectarian acharyas showing that the Shiva Purāṇa is the original, having a synonym as Vayu Purāṇa, due to Vayu’s major role (his role being the reason for the dual name). Additional detailed information is always welcome.
2. If the answer to Q1 is negative, then which text to mention as wrong and how would one sort the issues enumerated in point 2 above.

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^{Note: the colonial era mishap refers to the manner in which the colonists purposefully goofed around with traditional sacred Hindu texts, as stated by Ludo Rocher in his book, ‘the Puranas’. The result being, often not able to find verses quoted by other works or traditional acharyas in extant Puranas and heavy overlap in content (as shown above). Also one can get an example of the overlap between the Vayu and Brahmanda Purāṇa by looking at revision no. 3 here}