I 'm not sure of the relationship between these two bodies, but I gather that the College is a 'professional organisation' (a bit like a 'posh' Trade Union) for healthcare chaplains. The UK Board is more of a regulatory and registration outfit, it regulates and controls who is able to be a chaplain, and sets standards of performance for chaplains to follow. It's more of a "gate-keeper" organisation.
Doctors have the General Medical Council to regulate who can practice as a doctor, and it also sets standards of practice. All doctors who want to practice have to register with the GMC. If a doctor does something "wrong", the GMC calls them to account and may strike them off the register if found "guilty". The GMC is answerable to the Executive i.e. Parliament.
Doctors can also join the BMA (British Medical Association) - this is their 'professional organisation', it lobbies for better recognition, better pay and conditions, and represents the interests of doctors. If, for example, a doctor is hauled up in front of the GMC for malpractice, the BMA will help him to defend himself at a GMC 'hearing', provide him with a barrister, and counsel and support him, whatever way the case goes.
The UKBHC is like the GMC, the College of Healthcare Chaplains is like the BMA. It's the UKBHC that will eventually be answerable to the Executive. That's the way I understand it. I may be wrong and these things are still a bit fluid, but it looks like the way things are shaping up in healthcare chaplaincy.