There are three separate verses in different places in the Torah that all say the same thing - “You shall not cook a kid in its mother’s milk.” As with all repetitions in the Torah, the Rabbis find this to be highly significant and learn from it three things: the prohibitions to eat, cook and derive benefit from meat and milk of kosher animals cooked together. The phraseology of “kid” and “its mother’s milk” is simply the most extreme example of this prohibition, either because of its appearance of cynical cruelty or perhaps because it was a specific practice of idolaters, or even because it was most common to make meat/milk dishes from soft, younger animals - but the Torah is read to include all meat and all milk of domesticated animals. Although we translate גדי/g’di as “kid”, which in English implies a baby goat, the Talmud proves that in the Torah, it can refer in general to the young of any domesticated livestock (goat, sheep or cow), because in another context the Torah specifically mentioned “g’di `izzim” - a “kid of goats” as opposed to the “kid” of another domesticated animal.
As far as whether others interpret it differently, I assume anyone who does not accept the reliability and authority of the Talmud, as we do, will interpret it as he likes. I don’t know of specific examples.
Update: To clarify, although the Torah only forbids the meat and milk of sheep, goats and cows, the Rabbis also forbade mixing milk and meat of kosher wild animals such as deer and buffalo, as well as milk with chicken, to avoid mistakes. (Milk w/eggs is ok.)