I think that matching relates to cashflows, whereas hedging relates to asset / liability values.
So, for example, it might be the case that the asset and liability values move in line with each other, but that the cashflows are not necessarily matched.
I tend to think of liabilities being perfectly hedged where the assets actually define what the liabilities are, eg DC pension policies and unit-linked products, and would use the concept of hedging when trying to ensure a provider is solvent / funded. I would use matching when trying to ensure that the liability cashflows can be met.
So in practice, I think the two things might be pretty similar, but may apply in different contexts.