There are many types of bullfinches found in the world although none are native to North America. The Cuban Bullfinch and the Greater Antillean Bullfinch are both native birds to the West Indies Islands. These two dark plumaged bird species are found in the forests of the tropical islands and are often seen feeding on fruit.
Some bullfinches have been reported seen on the North American continent, and if so they were probably escaped or birds brought in by strong winds or storms.
Avibase - the world bird database This site provides the user with a complete list of bird species, broken down per country, or in the example of the US or Canada, per state and province. Here, bird species names are available in other languages, a great asset to be used as a translation of foreign bird names.
ABA - American Birding Association This site represents an organization that maintains official records of all birds species that have been proven to have been seen inside the perimeters of the North American Continent and the surrounding bodies of water. Regular revised versions are posted to keep the bird list current at all times. This is the list used by all serious birders over their lifetime. You may be aware of the movie called the "Big Year". It was with this list that all the competing birders used in an attempt to set a new record as to how many bird species that could be seen by an individual birder in one calendar year.
I hope you will take advantage of these suggested websites. I have used each of them, in one way or another, throughout the years in my quest to better identify and understand our fine feathered friends.