The word baẓr is generally used to refer to the glans clitoris. However, in shafiʿi fiqhi literature, the word is used to refer to both the clitoris as well as the clitoral prepuce. Early shafiʿi scholars did not use the term baẓr, instead they relied on a detailed physical description of both the clitoris and the clitoral prepuce. A small number of the later scholars used the term while others solely employed the description. Regardless of whether or not they used the term, there is no disagreement on what and how much is to be removed in the female circumcision operation known as khafḍ.
Imam al-Mawardi says:
"As for khafḍ of the woman, it is the cutting of the skin located in the uppermost area of the genitals, above the entrance for the penis and the exit for urine, on top of a base that resembles a kernel. In it [i.e. khafḍ], the elevated skin is removed, not its base." 
As we can see from this passage, al-Mawardi described the clitoris as a structure resembling a kernel/core of a fruit or a nut, and the prepuce as the skin that sits on top of it. He regards the clitoris and the prepuce as one structure, identifying the clitoris as the base [ar:ʾaṣl, which also means 'the lowest part of a thing'] and the prepuce as the 'elevated skin'. He does not employ the term baẓr, but he makes it very clear that the area that is to be cut is the prepuce and not the clitoris itself.
Imam al-Rowyāni says:
"There are two virginities that pertain to a woman: one of them is the hymen, and the other is that whose cutting is obligatory, and it is the crest of the rooster that is in the uppermost area of the genitals between the two edges. When it is cut, there remains its base resembling a kernel. At which point she is said to be makhfūḍa [en:circumcised]." 
In the above passage, al-Rowyāni likens the prepuce to the crest of a rooster; this analogy will be reiterated by most of those that came after him. He also ended the passage by confirming that the operation he described is known as khafḍ.
Imam al-ʾArdabīli says:
"The circumcision of a woman is by cutting the piece of flesh that is in the uppermost area of the genitals, above the exit of urine, resembling the crest of a rooster. When it is cut, there remains its base, resembling a kernel, and it suffices to cut a minute part." 
ʾArdabīli's wording is almost identical to that of al-Rowyāni but he clarifies how much of the prepuce is required to be removed. We shall see in al-Juwayni's passage below from where the jurists derived this understanding.
Imam al-Juwayni says:
"The required amount for women is a minute part, and there exists in the ḥadīth support for this: He, Allah's Mercy and Peace be upon him, said to the women performing the circumcision: ʾashmī which means to leave the area ʾasham, and the ʾasham is that which is elevated [i.e. not flattened]. And the cutting is to be done at the uppermost area from a piece of meat this is manifest" 
Imam Nawawi says:
"As for the woman, It [i.e. circumcision] is to cut from the flesh that is in the uppermost area of the genitals, above the exit of urine, and it resembles the crest of a rooster. When it is cut, there remains its base resembling a kernel, and it suffices to cut a minute part." 
al-Khatīb al-Shirbini says:
"Circumcision is obligatory upon the woman by cutting a part from the flesh that is at the uppermost area of the genitals, above the opening for urine, resembling the crest of a rooster. When it is cut, there remains its base which resembles a kernel. And it suffices to cut a minute part." 
Ibn Ḥajar al-Haytami says:
"The way it is done for the woman is by cutting a minute part from the flesh that is located in the uppermost area of the genitals, above the opening for urine, resembling the crest of a rooster, and it is called the baẓr." 
Ibn Ḥajar, in the passage above, as well as al-Ramli and al-Millibari all used the term baẓr, however, as previously mentioned, one should not understand from this that they are referring to the clitoris only; instead they, like all those who preceded them, are referring to a single organ composed of the clitoris, which Mawardi and others called the base, and the prepuce, which Rowyāni and others described as the crest of a rooster. In addition, those who used the term baẓr, when identifying the part that is to be cut, they referred to it as that which resembles the rooster's crest so as to exclude the glans clitoris that they refer to as the base that resembles a kernel. This meaning is conveyed very clearly in the passage of al-Khatīb al-Shirbini, who is a contemporary of both ibn Ḥajar and al-Ramli. Therefore, the usage of the term baẓr should not be taken in any way as a deviation from the established position of the Shafiʿi madhhab.
The small number of references I've shared with you are representative of the unanimity that exists on this issue, which is a testament to the authenticity of shaykh Nuh Keller's translation, may Allah preserve him and reward him for his contributions.
Allah knows best.
 al-Ḥāwi al-Kabīr, al-Mawardi (DKI, v16, p341, 1999)
Baḥr al-Madhhab, al-rowyāni (Dar al-Turāth al-ʿArabi, v13, p163, 2002)
al-ʾArdabīli, al-al-ʾAnwār (Dar al-ḍiyā, v3, p335, 2006)
al-Juwayni, Nihāyat al-Maṭlab (Dar al-Minhāj, v17, p355, 2007 )
al-Nawawi, Rawḍat al-Ṭālibín (al-Maktab al-Isami, v1, p181, 1991)
al-Shirbini, Mughni al-Muḥāj (DKI, v5, p539, 1994)
al-Haytami, Tuḥfat al-Muḥtāj (Dar Ṣādir, v9, p198)
Answered by: Shaykh Omar Mohsin