What is the most reliable distinction between a circumstantial and a parenthetical clause?

Iʿtirāḍ and the Relative Measure of Ījāz and Iṭnāb — Concluding Volume 1

• Their word counts
• The mandatory presence of wāw
• The circumstantial clause has an accusative position; the parenthesis has none
• Both occur only in the past tense