What is the difference between matching and liability hedging? I can't seem to see any difference between the two.
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.
Agreed. Matching is an example of a hedging technique, but there are other ways in which hedging can be performed which would not be cashflow matched. You might find the following previous thread useful as well: https://www.acted.co.uk/forums/index.php?threads/liability-hedging-vs-perfect-matching.4406/