Die chatter and double struck are two different things. If a coin is double struck, it has entered the coining chamber a second time or failed to be ejected after the first strike. It would then get struck a second time. Sometimes the second strike is off centre and sometimes it's centred but every time it effects both sides of the coin.
Die chatter is now referred to as Machine Doubling Damage in the US error market. Alan Herbert, a giant in US error circles, wrote, "The evidence is very clear that MDD occurs after the strike. The coin design is complete, meaning the die pair has done its job. The bouncing/chattering die moves metal that has already been formed. Struck metal has a different appearance than the metal shoved or moved by the bouncing die. Because of this difference it is possible to trace anything that occurs during the minting process. Anything that happens after the strike cannot be traced as to time or place."
MDD is characterised as flat, shelf-like doubling. It is almost always on only one side of the coin and it is almost always the hammer die.