Johann Friedrich Blumenbach (the father of physical anthropology) defined the "Caucasian" race as synonymous with "White", which in North America, "Caucasian" or "White" became synonymous of those of predominantly or full-blooded European descent, especially those who are not Hispanic.
Blumenbach also believed that the other races were simply malnourished, & that will the "right diet" they will return to the Caucasian race, as he believed that Adam & Eve were Caucasian, assuming based on his interpretation of the bible.
Strictly speaking "Caucasian" is someone Indigenous to the Caucasus region, Blumenbach believed that the "White" race originated in the Caucasus mountains, however recent genetic studies actually found the the ancestors of "Caucasians" actually originated in the Near East, & that West Eurasian is the most accurate term to describe that branch of humanity.
"Caucasoid" is simply an outdated term, & is no longer taken seriously in Genetic Genealogy & Physical Anthropology, although some older scholars still use the term.