Comments to the recent post on “potted,” meaning summarized or abridged, led me to understand that British people use the the word “pot” to refer to smallish containers for food, whereas for Americans, a pot is strictly the thing you cook in, frequently mentioned in company with pans. (British) Catherine Rose commented:
Potted food is in pots. It isn’t even always in a closed pot – potted shrimps are in an open-top pot which is sealed with a layer of butter, and has a very short shelf-life. Sometimes it’s in a ceramic pot with a ceramic lid, and sometimes in a glass jar with a lid that closes down with a seal (like a Kilner jar).
That made me remember that in Britain, a single-serving receptacle of yog(h)urt is called a pot, whereas I would just call it a container. (Being a native New Yorker, I would use the same word for the vessel in which you get coffee to go, properly pronounced “a containuh of cawfee.”) Some research confirmed this distinction. For example, consider this Google Ngram Viewer chart showing phrases’ frequency of use in books in the Google Books database:

I included British “container of yoghurt” in my search, but it doesn’t show up on the graph because, seemingly, that phrase has never appeared in a British book. The Brigham Young University Corpus of Contemporary American English, comprising 560 million words of text uttered or written in the U.S. between 1990 and 2017, allows you to search for the words that most commonly occurred before the phrase “of yogurt.” Here are the results:

“Cup”‘s 100 percent margin of victory over “container” is a bit misleading, I would say, because the word is also a unit of measurement (8 ounces), and is used that way in many of the thirty-four hits in COCA. But “cup” definitely is also used for a single serving (and not a measurement), as seen in this photo of a Dannon yogurt’s nutrition label I snapped at a supermarket. The serving size is listed as “1 cup,” but 150 grams is only 62 percent of a measuring-cup cup.

For additional research, I created separate Twitter polls for British and American people. Here’s the result of the British one.

And here’s the American one:

That 20 percent “Something else” response is a sign of a poorly designed survey. The Twitter comments revealed that the most popular other term was, you guessed it, “cup.” “Thing” and “carton” also got some mentions.
The question remains, is “tub of yogurt” a Not One-Off Britishism? The phrase occurs exactly once in the Corpus of Contemporary American English, in a 2007 New York Times article about a redesign of the 1957 Fiat 500: “In France, … the original 500 was lovingly known as the ‘pot de yaourt,’ or pot of yogurt, for its soft shape.”
But the 5 percent showing in my American Twitter poll, and its presence in the Ngram Viewer chart, suggests “pot of yogurt” is making a U.S. incursion. My daughter Maria Yagoda, the digital restaurant editor at Food and Wine magazine, wrote me that she felt “pot” had gained popularity in the last ten years or so: “Because ‘container’ just wasn’t a good, specific enough word so we jumped on the opportunity to use pot.” A few examples pop up when you search in Google News. Last year, in Elite Daily, American Jordan Bissell wrote, “Who wants a little plastic pot of yogurt when you can have a frozen stick full of delicious, nutritious goodness?” And in 2017, the Wall Street Journal published this headline:

Bottom line, expect to see more American “pot of yogurt.”