Considering that China grows nearly 13 times as much carrots and turnips* as the US, it’s likely that the Sam’s Club carrots came from China. It’s also possible that they were prepared in China and shipped here frozen.
I saw a YouTube video which showed a wild carrot root. It looked more like a tree root than anything someone would eat. According to Wikipedia, the carrot was originally grown for its aromatic leaves and seeds. Parsley, cilantro/coriander, fennel, dill, and cumin are close relatives and are still grown for their leaves and seeds. Old English did not clearly distinguish between carrots (which were white at the time) and parsnips**. The Moors introduced the carrot to Spain in the 8th century. In the 10th century, the roots were purple. The modern carrot originated in Afghanistan around that time. A Jewish scholar mentioned red and yellow carrots in the 11th century. Cultivated carrots appeared in China in the 14th century and in Japan in the 18th century. Orange carrots appeared in the Netherlands in the 17th century.
*Turnips are related to rutabagas, cabbages, mustards, radishes, broccoli rabe/rapini, bok choy, and Napa Cabbage.
**Parsnips are closely related to carrots as well as parsley. Parsnips were used as a source of sugar before cane and beet sugars became available. Parsnips were replaced by potatoes as a main source of starch.