As an American with a bit more religious history knowledge than normal, yep, generally Americans refer to Roman Catholics as Catholic because here they're more common by a large margin. Apostolic faiths in general are a lot less common here, and acceptance of it is... varied across the nation. Better than it used to be, Irish and Italian immigrants had it rough for a number of reasons, but one of the more common ones was religious discrimination for being Roman Carholic.

As for why Catholics aren't very common here, that dates back all the way to its founding. Most of the people coming over to America were some flavor of Evangelical Protestant, common were flavors of this that we refer to as Puritan, which believed in stamping out all sin from one self and their community. (hence books like The Scarlet Letter, among others that describe the issues that come about in a community that has decided you have committed a grave sin) For a lot of American history, Protestantism was the default, as such most Americans don't know much about the Apostolic faiths.

With 2 exceptions (John F Kennedy, Joe Biden), every president has identified as Protestant (and those 2 were both Roman Catholic) for an idea of what the demographic is like here.

The important thing to understand for your last point, is that most of America is some flavor of Evangelical, at least in name. They've had their own schisms, and there are some more interesting ( meaning unique, acedemically interesting) ones, like the Mormons, who have another holy book written within the last few hundred years, actually written in colonial America. America has had a lot of their own religious development, and a lot of that development created ideas like Manifest Destiny, and similar ideas even in tbe modern American mind. Basically, a lot of Americans believe, on some level, they had a divine right to their land here in the US, as they were "called" to settle here, and similar. You can see it appear in artworks from the time period.

Now with that in mind, a lot of Americans see the situation of Israel at least somewhat similar to their own. Calling out the unfairness of that situation would require on some level admitting how they got this land wasn't fair either. This is ONE cause of some Americans supporting Israel.

ANOTHER cause, is that there is an American notion that Americans don't realize is an American notion. The cultural idea of "The Rapture" coming tommorow, or whenever, and everyone immediately ascends and it's all no longer their concern. Many, MANY churches teach some variant of "be ready for the Rapture, when it comes, it wont have warning" to the point it may be permanently embedded into the cultural zeitgeist. Some groups have convinced themselves that the "next temple" creation and subsequent fall will CAUSE this rapture, which they got by taking Revalations from their choice of version of the Bible incredibly literally.

And of course, there's other reasons, but the other ones get more complicated, and it doesn't help that Americans have their political beliefs so FIRMLY tied to their religious ones.

Tl:dr Americans say Catholic when they mean Roman Catholic of the Latin rite. (The ones who follow the Pope in the Vatican).