Brahman has multiple meanings. As shown from the verse quoted in the question, it is effulgence of Krishna's body. But it also refers to unqualified absolute or what you termed as impersonal brahman. Then it is very close to Advaita Nirguna brahman with some difference.
vadanti tat tattva-vidas tattvam yaj jñAnam advayam brahmeti
paramAtmeti bhagavan iti sabdyate
Knowers of reality declare that reality to be nondual consciousness,
called “Brahman,” “Paramatma,” and “Bhagavan.”
Jiva Goswami recognizes the fact that the three designations are often used interchangeably
in texts; the BhAgavata mentions them here in order to indicate
their primary significance. The selection of names is not arbitrary; the verse
does not, for example, give “living entity” (jiva) as a name of the nondual
reality. Nor is the order in which the names appear random. The BhAgavata
PurAna is indicating a hierarchy of forms from Brahman to Bhagavan, based
on the degree of revelation.
Bhagavan is the complete manifestation of the
nondual reality and, indeed, identifiable with it.
In him, all the inherent energies (saktis) of the Supreme are clearly visible—beauty, power, wisdom, majesty, abode, and associates.
Then, depending on the degree to which the
fullness of the Lord’s glory is hidden, he is known as either Brahman or
When Bhagavan’s energies are manifest in a partial way, mainly
in regard to directing material nature ( prakrti) and the living entities ( jivas),
he is known as Paramatma—the inner controller, inspirer, and support of
"When his attributes are totally unmanifest, he is known as
Brahman—the undifferentiated, unqualified, and impersonal Absolute."
“That which is not qualified, and which shines because it is pure consciousness,know it to be
It is important to observe that the hierarchy proceeds “top-down” rather
That is, although Brahman in this scheme appears very
similar to the qualityless (nirguna) Brahman of the Advaitins, in fact, Brahman
here is not the essential, most fundamental form of Reality, upon
which various attributes must be “added” in order to “get to” Bhagavan.
Rather, Bhagavan in all his fullness is the starting point for the Gaudiya
concept of the Supreme. Brahman is Bhagavan, but with the splendor
and glory supressed.
However, in non-conventional usage Brahman refers to Krishna.
In his instructions to Sanatana Gosvami at Kasi, Caitanya explains the
implications of the “vadanti” verse:
The word “Brahman” refers to Svayam Bhagavan, who is one consciousness
without a second, and without whom there is nothing else. “Knowers of
reality declare that reality to be nondual consciousness, called
‘Brahman,’ ‘Paramatma,’ and ‘Bhagavan.’” That nondual reality is
Krsna, Bhagavan himself. He exists in all three phases of time (past,
present, and future). This is evident from the scriptures. . . . The
word “AtmA” refers to Krsna. His nature is greatness [brhattva]. He is
all pervading, the witness of everything, and the supreme form . . .
Although the words “Brahman” and “AtmA” refer to Krsna, by
conventional usage they refer to the Undifferentiated [nirviSesa] and
the Inner Controller [antaryAmI], respectively.
Ref: Chaitanya Vaishnava Vedanta by Ravi M Gupta.