I see a distinction. A cultural hub tends to be multi-tenancy specific and something that's not necessarily within four walls. It might have multiple buildings, but it tends to be under one governance structure, and there would be programming within that hub. The cultural district is more a geographic area and so would have multiple entities and organizations, with a mix of for-profit and non-profit but all within a district.
In music, of course, we deal with a lot of municipal regulations. There are, for instance, noise bylaws, etc., and a municipality can designate specific regulations and bylaws just for that district in order to encourage more of those cultural uses. That, to me, would be the distinction between the two.