I am a tenor who has been singing with an older woman who has not been classified vocally other than that she should sing alto in school. So she could be both a mezzo-soprano or contralto. So I have this question: If a woman singing together with a tenor sings the same pitches as the tenor does that mean that she is a contralto?
The human voice is not like other instruments. You can learn to play a tenor sax or an alto sax (or both) and they are effectively different, but similar, instruments. There is overlap, but they are distinct.
The human voice is the human voice. You don't learn to sing tenor or alto or contralto or anything else. You just learn to sing and you have your own range. Your part depends only partly on your vocal range, but also on your preferences and what is needed. At one point in college I sang bass in one choir, tenor in another and alto in a third. So what was I? Even though my natural range in more in line with a baritone, I choose to call myself a tenor, because that is what I prefer to sing and it is well within my ability. But, in the end, I am whatever part I happen to be singing at the time.
My point is, you can't really classify her as any particular part. I'm guessing she is able to sing alto just fine, so she could be that (with an extended low range). In other situations she may well be a contralto, but she could also be considered a tenor if that is the part she is singing. It is dynamic and fluid and changes depending on context.
Since contralto is considered the lowest female voice, and tenor the highest male voice, and the range of each is similar, loosely, then yes, that's about the only label that will fit, loosely.
The lower part of a lot of tenors' range is lower than that of most contraltos, and certainly the quality of sound produced often won't match, and the same could be said about the higher part of the tenors' range in comparison to that of contraltos. There are, of course, always exceptions to the 'rule'.
My big question is why we seem to have the desperate need to label, when there's such a disparity in singers' ranges anyway. Whilst they're instruments in their own right, they won't ever have the sort of 'exact' range of man-made instruments, like a guitar has a range of 4 octaves. Sorry - it could be argued that voices are 'man-made' too!