Please try some peas.
-- Mmmm. These peas are delicious! Do you have a secret recipe?
I'll let you in on the secret: my grandma's recipe calls for a generous dash of arsenic.
-- They're scrumptious. I've already eaten the first helping you have given me.
Well then, have a second helping. But I doubt you will ask for a third.
Why do we say "the first helping" but "a second helping"?
The first helping is a particular helping: it actually existed, and was of a certain size and taste and color and temperature, and so forth, and it was served to you at a particular time.
A second helping, on the other hand, is only a possibility, a concept, an abstraction: "a-helping-that-would-come-after-a-first-helping". Its only attributes or properties are its ordinal and its category.
In the same way, "a second season" means only "a season that would follow upon the first season". Until it acquires some specific properties in addition to its ordinal (2nd) and its category (season), such as plots and stories, new characters or reappearing characters, a number of episodes, whatever, we cannot speak of "the second season".