What is the difference between the two wordings and which one is correct?
(1) Why is past tense not used?
(2) Why is not past tense used?
What is the difference between the two wordings and which one is correct?
(1) Why is past tense not used?
(2) Why is not past tense used?
You can choose either of the two
Why is past tense not used?
or
Why isn't past tense used?
(1) Why is past tense not used?
This is correct, but the sentence places an emphasis on the fact that past tense was not used, and suggests a belief that perhaps it should have been.
(2) Why is not past tense used?
In this construction, "is not" should be replaced with "isn't."
Both are incorrect, but if you inserted the word "the", the first one would be correct, while the second would still be wrong:
(1) Why is the past tense not used? (correct)
(2) Why is not the past tense used? (not correct)
"Not" modifies "used" rather than "the past tense": "Is the past tense used?" "No, the past tense is not used." Adding "Why" to the beginning of a sentence pulls the auxiliary verb into second position, but leaves "not" and the other words where they were.
UPDATE: As pointed out by @user3081485, you could also write:
(3) Why isn't the past tense used?
They are both correct, but the first one sounds more natural. An even better phrase would be, 'why isn't past tense used?', because it flows better.
You know that we have the S-V inversion in most questions in English. In your examples the subject is (@Alan) the past tense, so we would invert that and is. "Why is the past tense not used?"
However, contractions have to stay together, so we'll invert "the past tense" with the whole contraction: "Why isn't the past tense used?"
See here for a bit more information Wikipedia on Contractions and Inversions.