To perceive is to become aware of something directly through the senses. To conceive is to form something in the mind or to develop an understanding. So perceiving is merely seeing, and conceiving is deeper.
But perception often involves passive evaluation, and this is where the line between the verbs perceive and conceive becomes blurred. Think of perceptions as relatively shallow interpretations, and conceptions as more creative interpretations involving substantial thought or imagination.
Of course, a separate definition of conceive is to become pregnant. This actually helps in remembering the other definitions of conceive; all conceptions are acts of creation.
Perceive is correct in these sentences because the action does not involve deep thought or imagination:
… countless Americans continue to perceive big cities through the lens of 40-year-old movies like Taxi Driver and The Out of Towners … [The Atlantic]
Each was asked to stand outside and try to perceive different objects such as a car, a flag pole and a tree. [Daily Mail]
No one wants to be perceived as less than hyper-vigilant about the safety of our children. [Globe and Mail]
And conceive is used well in the following examples because the action does involve deep thought or imagination:
In modern hip-hop, it’s hard to conceive of a job more laborious than backing up Afrika Bambaataa’s record collection. [Chicago Tribune]
It’s hard to conceive what that would be like. [Stuff.co.nz]
But five years after first conceiving the idea, museum chairperson Brannen opened the doors to the Vidalia Onion Museum last Friday in Vidalia, GA … [Independent]
Misconception vs. misperception
Misconception and misperception are both useful, but they’re often used in place of each other. For example, the so-called misconception in the following sentence is actually not a mistake of imagination or thought, but rather one of perception, so misperception would be more appropriate:
It’s a misconception that the most consistently challenging British artist of the past 30 years is, in her own words, a “weirdo recluse” … [Sydney Morning Herald]
Think of a misperception as a mistaken impression—for example:
Contrary to common misperception, the area is not rich with oil, although lucrative oil fields do lie just beyond its borders. [NPR]
And a misconception is a mistake of imagination or interpretation—for example:
… haters and super-fans both adopt an identical misconception: a belief that the whole phenomenon … is somehow the responsibility of the amiable teenager who fronts it. [Guardian]