The term “Coercively Assigned X At Birth” was coined by the trans community as a replacement for “Male to Female” and “Female to Male”, both to be more inclusive of nonbinary trans people and also to emphasize that trans people’s identities are not defined by their birth assignment.
“Coercively Assigned” terminology was not used within the intersex community to any appreciable extent until after it was firmly established in the trans community and had started spreading into the wider LGBTI community through trans activism. At that point, intersex activists — mostly nonbinary intersex people — began to cross-adopt it in the context of acknowledging the connections between trans people and intersex people. Note that this was before the emergence of scientific evidence indicating that transsexuality is in fact a neurological intersex conditions; it was based purely on recognition that trans people and intersex people were fighting very similar struggles for personal autonomy and self-determination against the system of birth-assigned binary gender.
The claim that trans people “stole” this terminology from intersex people is revisionist bullshit originating from intersex activists who bitterly opposed solidarity with trans people. There is no truth whatsoever to this claim.