As an informal turn of speech, it can be used to show that two or more parties are talking about basically the same thing but not in same exact terms, or not quite agreeing on the specifics.
Yet written down as tomato-tomato or potato-potato it looks just plain wrong and confusing (like in the video title above). Short of using the transcriptions /təˈmeɪtəʊ/ – /təˈmɑːtəʊ/ and /pəˈteɪtəʊ/ – /pəˈtɑːtəʊ/, is there a way of writing it down that indicates the differences in pronunciation?
It appears that there is this story behind the difference in pronouciation: Tomato:
Because of the song, tomayto, tomahto has come to be used as an expression meaning “unimportant difference.” The tomato originated in South America. The Spaniards first brought tomato seeds to Europe in the 1540s. The seeds produced a yellow tomato. Because of the color, an Italian botanist called it pomo d’oro, “golden apple.”
So what about the English pronunciation? When the first tomatoes were grown in England in the 1590’s, Shakespeare (1564-1616 ) was a young man. The Great Vowel Shift, which began in 1450, was in full swing.
At some time in the eighteenth century, speakers in southern England began pronouncing formerly short a words like half, calf, laugh, after, path, aunt, and can’t with the broad a of father. At first the broad a pronunciations were considered “substandard,” but they eventually made their way into the standard speech of the upper classes. Not everyone found them acceptable.
Writing as late as 1921, H. L. Mencken mentions an English contemporary who felt that the “tomahto” pronunciation was “pedantic” and not to be preferred to “the good English tomato, rhyming with potato.” Nowadays “tomahto” is considered British pronunciation and “tomayto” American, but many Americans pronounce tomato {and aunt ) with a broad a. Either pronunciation is considered standard. The only “rule” is to go with the pronunciation you prefer. Either is easily understood by other English speakers.