Are there alternatives to Bitcoin which take a different approach?
There are "digital bearer certificate" systems, which are an older concept.  They require a centralized issuer in order to prevent double-spending.  You can think of the certificates as electronic IOUs for a commodity (such as gold) held by the issuer.

Some DBC systems implement Chaumian blinding to anonymize transactions.

Open Transactions is a recent DBC system that has gained some interest.  It could be used with Bitcoin as a backing commodity, taking advantage of the properties of both systems.