Nope. They are different. Sweet tea is made with sugar added during the process of making it, no? Sweetened tea is just brewed tea with sugar added after it is already done.
When a fluid is hot, it can have more salt or sugar dissolved into it without it falling out. (Science, bitches) That's why actual sweet tea is sweeter than brewed tea that has sugar added to it afterwards. Most restaurants outside of the deep south will only serve sweetened tea. Which is in fact, unsweetened tea that you add sugar to at the table.