Like you said, society's version of morality. So it can be a very important distinction because your own version of morality might differ. Not being aware of this distinction is dangerous because it stops people from developing their own moral compass. This own morality is more firm and can be relied on in the absence of shame, or even when society encourages behavior one finds immoral.
I'm even gonna go on a wilder speculation here and claim that one of the driving factors behind humanity's worst atrocities was that large portions of society who had the potential in them for a firm morality rooted in empathy and love never developed this potential.
On a less import note, not being aware of this distinction can breed a lot of resentment and unhappiness, if someone is constantly compelled to follow rules that they, deep down, consider to be bullshit.
Of course that doesn't mean I encourage people to just disregard society's version of morality and lightly assume that they know better.
Edit: just noticed your username, I hope that furriosa is doing well <3
Deeply obscure reference