The uniqueness of one’s voice is attributed to genetics, coupled with the physiological development experienced as your body matures from childhood through adolescence, and into adulthood (especially with the onset of adult hormones and puberty).
The quality and care of one’s voice can also affect the unique tonality (timbre) that characterizes individuals, by their physical environment (exposure to allergens, for example), personal habits such as smoking, loud speech (habitual shouting), and other conditions that may strain or otherwise affect the vocal apparatus.
In response to the second part of your question, the next quote is taken from a somewhat trustworthy source, and describes the voice in terms of “resonators”:
”...There are seven areas that may be listed as possible vocal resonators. In sequence from the lowest within the body to the highest, these areas are the chest, the tracheal tree, the larynx itself, the pharynx, the oral cavity, the nasal cavity, and the sinuses.”
Based on my professional background knowledge of voice production (I’m a classically trained musician, an audio engineer, and professor of audio and media production), the actual production of one’s voice and speech is a product of several factors and processes that utilize the above named parts as a single apparatus:
-The size of the bones in your body (sound of your voice resonates from several areas of your body, not just from your voice box);
-The efficiency of one’s breathing (your lungs and diaphragm), as the chest cavity resonates with the vibrations produced by our vocal cords);
-The size and shape of the larynx (voice box and vocal chords) and pharynx (neck and throat), the size/shape/length/thickness of the vocal cords, the resonance and amplification from the nasal cavity, and lastly, the speech and enunciation that is produced by the oral cavity (mouth, tongue, lips and teeth);
-Your mastery in controlling the vocal cords to produce pitch in various registers (high-low, as in bass-baritone-tenor), your mastery/control of the throat and oral cavity, all of which separate trained singers from non-singers;
-And the physical act of voice production which produces speech/language, identified by one’s speech pathology; that is, the psychological and physical development of voice and speech, that can determine the sounds of one’s vocal patterns/inflections, accents, regionalisms and dialect.
Lastly, the developmental aspects of voice production and speech/language can be greatly influenced by one’s environment, education, cultural, social, ethnographic, and familial influences, and are measured, for the most part, in terms of psychological and social development.