Both are well explained on wikipedia, especially qiyas:
Istislah (Arabic استصلاح "to deem proper") is a method employed by Muslim jurists to solve problems that find no clear answer in sacred religious texts. It is related to the term مصلحة Maslaha, or "public interest". (wikipedia)
Note that Istislah is only applied if there's no text or a deduced ...
Qiyas is not a bid'ah since it does not satisfy the conditions of a bid'ah.
Sources of legislation in Islam
Sources of Islamic legislation are the Qur'an and the Sunnah of the Prophet (ﷺ). Al-Shafi'i said in his book "Jimaa' Al-'Ilm" (جماع العلم):
ولا يلزم قول بكل حال إلا بكتاب الله أو سنة رسوله (ﷺ) وما سواهما تبع
No point of view is binding ...
Ahmad ibn Hanbal didn't reject qiyas, but he rarly used it i've just read a paper called إقناع الناس بقول الإمام أحمد بحجية القياس (Convincing people that Imam Ahmad confirmed the authenticity of Qiyas) which extracted 6 examples of him using qiyas in his book masail al-Imam Ahmad and was presented in this Arabic thread.
But this small amount of used ...
The difference is simple.
Aql (intellect) is deductive logic e.g. you start with a general law from the Quran or Sunnah, then deduce a new ruling on a specific example that is covered by the general law.
Qiyas is inductive logic, this is where you start with a ruling, try to guess the general law, then apply the general law to a new specific case.
Istislah is to consider whatever is best for the common good of society.
Example: In Morocco, a girl was forced to marry the man who molested her. The judge used the idea of Istislah as an excuse for it as the man had done sexual things to her. (Maliki example)
Qiyas is to take a legislated ruling that is specific to a matter and make it general; as in ...
Qiyas and fiqh are more of a rational thing with base and argument and conceptualization rather that experience or wijdan ( I do not mean anything Sufi, I just mean like in the same way that you know justice is good, you know that aiding your parents is good, etc)
Aql can do Qiyas but it’s more of a light... whatever you put it to it shines. It tells what ...