What is the difference between a conception of something and a theory of something? Is the conception more extensive in content or less?
Example: iterative conception of sets and ZFC
I think conception of something generally refers to those things that we abstract from approved writings or sometimes through unreliable source which might not be authentic.That might be a reason , we sometimes realize that we are understanding that particular thing differently than what it really is.Conception of something depends on our way of understanding that something and setting it in our mind.
Meanwhile, theory of something is proved, reliable ,authentic, practised writings which is outcome of long term rational analysing and processing of different hypothesises .Theory of something might be universal as well.Its one of the major sources of gaining conception of that thing.
Making conception of a thing is a lot easier than making it recognised as a theory.