Unless they explicitly advertise abortions, they're not fake. "Crisis pregnancy centers" accurately describes what they do. Abortion clinics have tried to use euphuisms to hide what they do, which is why there's confusion. Given the aggression that is directed at abortion clinics, it's understandable why they'd want to use a vague description but not everyone with an unexpected pregnancy wants an abortion and the abortion clinics have created a situation where there can be confusion about what type of clinic one can expect based on the vague descriptors.
