(The following may not apply outside the Southeastern United States, aka “The South”.)
“Sweet tea” is specifically Orange Pekoe* tea with a minimum of “enough sugar to give a British person apoplexy”. Sometimes the Orange Pekoe is mixed with other black teas and/or an additional flavor such as Peach or Raspberry. Some lemon is allowed, but if you add too much it becomes Lemonade Tea**. “Sweet tea” is usually iced, but sometimes just chilled, and can be bought in cans or jugs***.
* known in (at least) The South as “tea.” If you asked most drinkers if they liked “Orange Pekoe Tea”, they would not know what was meant, and many might go so far as to ask “Is that like Lipton or Luzianne?” Just… say “yes” and move on.
** Not to be confused with the “Arnold Palmer”, which is three parts unsweet tea and one part actual lemonade. In the case of an Arnold Palmer, the Lemonade sweetens the tea. I would say that the Arnold Palmer is a perfectly respectable beverage, but not “sweet tea”, but I was raised in Alabama.
*** You can also buy cans or jugs of “Iced Tea”, but that’s marketing departments for you.
Note that “Iced Tea” and “Sweet Tea” are overlapping categories, but “Unsweet Tea” is absolutely a thing, and is almost always iced. Although there are, in fact, people who drink “unsweet tea” as ordered, it is very often an excuse for the drinker to take care of the sweetening themselves because they don’t know who decided how sweet the tea would be***. (Alternately, they want to use artificial sweeteners.) Some restaurants avoid this problem altogether by just serving “Unsweet Tea” and having a shaker of sugar the size of a 20-ounce beer can on the table. Meals served in these restaurants usually subtract from your total lifespan, but are also usually worth it.
Also, while it’s easy and entertaining for us to mock the Brits on their tea choices, it’s worth noting that when it gets into the high 70s there, it’s considered a heat wave and people die, whereas that’s a moderate summer day in Virginia. I suspect if I lived in a place where a 75F day in August was considered unusual, I might drink my tea hot more often.