I grew up in the suburbs of NYC, where there is a substantial Jewish population. There, it was understood that the "Holidays" were Christmas and Chanukah.
It was not just a matter of how merchandise was advertised. People actually wished each other Happy Holidays.
@DrWatson "Happy Holidays" is an American expression (first used in the 1860s), apparently - not really recognised in the UK where we have been using "Merry Christmas" since the 16th Century. My grandparents (both sets) lived in Whitechapel in the East End of London - the Jewish ghetto effectively - and they would not have recognised it either. Two nations divided by a common language.
@ArtieKat When Jews first immigrated to New York City, they tended to gravitate to particular neighborhoods -- "ghettos", so to speak. But by the time I was a kid growing up , Jews had moved to various suburbs and to other areas of the city. They no longer saw themselves as part of a ghetto. They had the expectation that they would be treated on equal footing with non-Jews in the society around them. This would NOT have been true of Jews in some other areas of the United States during the same time period, who had to endure societally accepted discrimination. That is why my response was very specific to a particular geographic area of the U.S. I don't think any Christian in the American deep south at the time would have ever said "Happy Holidays".
This might not be an example of the difference between UK English and US English (of which there are several) as much as it is an example of how English in both countries tends not to accommodate people with "ghetto" status.