I don't believe that there is a specific halachic status attached to the term "goy" as there are various definitions of this term, historically, as well as currently. I have summarized the definition / distinction:
Wikipedia outlines the history and usage of the term "goy". In Rabbinic terminology, it came to refer to Gentiles as a group. In modern language such as Yiddish and Hebrew it has come to refer to any individual non-Jew rather than the group collectively. Wikipedia states:
Maimonides defines "goy" in his Mishneh Torah as a worshipper of
idolatry, as he explains, "Whenever we say "goy" literally, we mean a
worshipper of idolatry" (Hilchot Ma'achalot Assurot 11:8
A Ger Toshav is:
a term in Judaism for a gentile living in the Land of Israel who
observes the Noahide Laws and certain religious and cultural
traditions under Jewish law and is therefore commonly deemed a
righteous gentile (Hebrew: חסיד אומות העולם chassid umot ha-olam
"Pious People of the World").
Based on these 2 definitions, except for the Maimonides one, the Ger Toshav would be a subset of the "goyim" group. If you used Maimonides definition,the Ger Toshav is not a "goy" since he is not an idol worshiper.
Halachically, then, the Ger Toshav follows the Noahide principles which, even "goyim" are supposed to do, anyway. The distinction, I don't think is in the halacha per se, but rather, which one of these is actually obeying what should be done.
See this related M.Y. question.