My sense of the term is that it is intended to be inclusive: not just black people but also Asians, South Pacific, Native American extraction, etc. so it’s not referring to the same group of people.
In some contexts PoC is appropriate because it is pretty much catch-all for "not white" (where "white" is used the same way as in "white supremacy", referring to a racial category defined by the absence of other racial identities).
In other contexts it is more precise to say Black because Black people experience a specific form of oppression by being Black, not just non-white. The same is true for other identities (like Indigenous) that are also part of the BIPoC umbrella, of course, but this is why it is often rendered as BIPoC rather than simple PoC.
