Thank you, AlpheccaStars. This is clear to me now.
I see 'a tea' is not correct. I thought an uncountable noun can be used with an indefinite article implying a meaning like 'a cup of tea' in the example, but I was wrong. Would you say, then, that the examples below are not correct? I hear these sometimes.
I'll have a Coke, please. Coke used to be sold only in distinctive specially-shaped bottles. So asking for "a coke" was asking for one of these, and it just caught on. At the fountain, I say "I'll have (a medium (sized)) Coke." I'll have an orange juice, please.
As I said, it is based on history when Coke used to come in Coca-Cola bottles. When you ordered "a coke" you didn't mean an amount of liquid, you mean a chilled bottle with the liquid inside. These days, you almost never see the classic coca-cola bottles. But the old way of ordering it has stayed in the culture - I'll have a coke.
Perhaps for the first time, I disagree with A Stars. I would easily interpret "a tea" as a cup/glass of tea.
When I was waitressing the breakfast shift, it was common enough to get an order for "two coffees and a tea" or "two teas and a coffee" (or whatever combination). (At breakfast, "a tea" would get you hot tea.)
(Once it was the lunch shift, "two Cokes and a tea" would
That's interesting, because I consider "tea" to be non-count and have always ordered "a glass of iced tea/iced tea," "a cup of hot tea/hot tea," or "a pot of tea."
I suppose if you're in the waitressing business, there would be lots of short cuts - "two teas" glides much faster off the tongue than "two glasses/cups of tea."