Un autre son de cloche

Literally, the expression translates into another (a different) bell sound.
When you strike or shake a bell, how many different sounds come out? Only one. To get another sound, you need another bell.

The same applies to a debate or a controversy: you need to hear more than one side of a story - or one bell sound - to get a full picture. That is the idea: un autre son de cloche means another perspective about, or a different version of, a controversial event.

You would use it primarily in the context of a conflict, or a debate, if you want to emphasize one of two situations.  Either you suspect there might be more to a story than what is provided, or there seemes to be a consensus about the matter at hand, until someone brings up a different version that contradicts the former.  You would then describe that "other view" as a different bell sound, a different tune.

You might hear it as an exclamation:  Ça, c'est un autre son de choche! - This is a different story!  Or as an object to a verb, such as: J'aimerais entendre un autre son de choche sur ce sujet - I'd like to hear about another side of the story (because I suspect there is more than one.)

The expression un son de cloche is just a synonym for a one-sided story, when referring to the perspective of a group, in the absence of other perspectives.

Origin

This expression comes from an old proverb: Qui n’entend qu’une cloche n’entend qu’un son – Who hears only one bell hears only one sound.

In this proverb, the bell is compared to a single speech from which a decision should be made. Quotes from the 16th and 17th century indicate that the proverb was mostly used in reference to justice - or lack thereof - whenever public opinion suspected that justice had been brought without hearing all parties involved. Or even worse: when the opposing party had been outwardly silenced.

The proverb as such is no longer in use.  Only the metaphor of the bell sound has survived to this day in French.

Examples

D'après le gouvernement, tout va bien,  mais du côté des économistes, c'est un tout autre son de cloche.
According to the government, everything's fine , but we are hearing a completely different story from economists.

C'est là un son de cloche très différent de la propagande habituelle!
This tells a very different story from the usual propaganda!