Here are the ranges defined largely as they apply to classical singing:

Every single tone in singing has a frequency spectrum. The vocal cords create a vowel sound. The cavities' resonances above the cords (pharyngeal, oral, nasal) shape the spectrum. These resonances are called formants. 

Formants for various vowels. From Brixen, Eddy B.: Audio Metering, 3rd edition, Routledge 2020.

The pitch of a tone can be kept constant, and the vowels can be changed by modulating the cavities.   
Many singers (classical singing) may add a so-called singer formant. This additional resonance is typically around 3 kHz. The effect allows the voice to cut through the sound of the accompanying orchestra. In other genres, like pop/rock, the phenomenon is called a metallic sound, a color added to the neutral voice. 

Example of singers formant (dashed line). After Sundberg, J. (1987): The Science of the Singing Voice. Northern Illinois University Press. (p. 123). 

For engineers, it is worth knowing that high-pitch singing may change the sound of vowels if the lower formants of the given vowel are below the pitch of the note being sung. This happens in all genres of singing. 

Male singing a vowel: “EH” [ ] in the CVT-mode Overdrive. F1/F2/F3 are plotted against pitch. The dashed line shows the frequency of the pitch (f0). It can be seen that the frequency of the first formant significantly increases with increasing pitch. (From Brixen, Sadolin & Kjelin: Acoustical characteristics of vocal modes in singing. AES Convention 134, Rome, Italy. Preprint 8897).