Does the phrase "analogy with a difference" (قياس مع الفارق) convey the same meaning as the phrase "contrary to analogy" (على خلاف القياس)? If not, then what is the meaning of "analogy with a difference"?

"Contrary to analogy ( خلاف القياس)" means to establish a ruling for something that differs from the ruling of its parallels, based on evidence. Linguists often use this term to refer to what is heard (from native speakers) and deviates from a rule. As for "analogy with a difference (قياس مع الفارق)," it means that an analogy was made but was invalidated due to the presence of an impediment, which is the complete absence of the original's underlying cause in the new case.