Unified Commerce to me appears to be when one uses an OMS as it should be used, as the single source of the truth. The truth for customer, product, inventory, pricing & promotion, tax, auth transactions, and shipping. In this case, existing enterprise systems are integrated in to the OMS using an enterprise bus like IBM Integration Bus (IIB) that does the enterprise systems to OMS data translations.
I guess now, one would say the ideal of “OmniChannel” is using chewing gun and duct tape to integrate disparate systems, so in that case there may as well be more than one source of the truth.
However, it’s all marketing spin, as the practitioners I know and worked with implementing globally distributed OMS/EOM systems will think the former was always the way…and would have called it OmniChannel.