First, when scripture usually (but not all the time, since the use of the feminine and masculine to a noun or pronoun is usually arbitrary) refers to Brahman in Sanskrit the neutral singular Brahma[n] is used. And most of the time when the masculine singular Brahmā is used it refers to Brahma[n] in His creative aspect as the four headed Creator. Sri Ramunja in his Sri-Bhasya to the Brahma Sutras says in his commentary to verse I.I.1 (translation by Swami Vireswarananda p 1):
The word ‘Brahman’ is derived from the root ‘brh’ which denotes greatness, and is therefore applicable to all objects which have the quality of greatness, but more aptly to that object which by nature and by qualities possesses this greatness to an infinite degree; hence the word ‘Brahman’ primarily denotes that supreme Person who is the abode of all auspicious qualities to an infinite degree and is free from all worldly taint. This supreme Person is the only Being the knowledge of whose real nature results in liberation.
In his Introduction to his translation of the Bhagavad Gita with the Commentary of Sankaracharya, Swami Gambhirananda writes on page xv:
…the Krsna of of the Mahabharata, otherwise known as Vāsudeva (son of Vasudeva and Devaki)…
And in a footnote to the above (p xv):
Vāsudeva is mentioned first in the Taittiriya Aranyaka, 10.1.6, ‘as a god together with Narayana and Visnu, apparently as mystically identical with them.’ (H. Jacobi, Encyclopedia of Religion and Ethics, vol. vii, p. 195.)
In agreement with this we see in the Mahanaryana Upanishad pp 45-6, verse I.29, translation by Swami Vimalananda:
May we know Narayana. For that, may we meditate on Vāsudeva. May Visnu impel us towards it.
And in his commentary on this verse he writes:
The Highest Person is here supplicated as Narayana, Vāsudeva and Visnu. Until and unless He impels the individual Soul, it cannot contemplate Him, and without contemplation on Him, His true nature cannot be understood. The etymological meanings of the three epithets are given at length in the bhasyas on the Gita and Visnusahasranama. Bhattabhaskara’s explanation of these words in the Visnugayatri is noteworthy. He derives Narayana thus: The term Nara, being derived from the root nr to lead, means the leader of all creation. Nara derived from the above word denotes his offsprings. Narayana therefore, is the effective cause of all creatures. Thus Narayana is Paramatman. He is called Vāsudeva in his immanent aspect, i.e., dwelling in all creatures as Antaryamin. The term Visnu implies His all-pervasiveness.
And at the end of his Introduction to the Gita, Sankara writes p 7 (Swami Gambhirananda translator):
This scripture, viz the Gita, while particularly revealing the twofold dharma having Liberation as its goal and the supreme Reality, Brahman, called Vāsudeva, as its subject matter,…
In the Gita Krishna refers to Himself several times as Vāsudeva. For example, in verse 7.19 the Lord says:
At the end of many births the man of Knowledge attains Me, (realizing) that Vāsudeva is all. Such a high-souled person is rare.
Thus, Brahman and Vāsudeva both refer to that same Supreme Godhead or Supreme Person of the Godhead.