Quasi-contract
The terms quasi-contract and contract implied in law are synonymous. There are two types of quasi-contract. One is an action in restitution. The other is unjust enrichment. Note, therefore, that it is improper to say that quasi-contract, implied in law contract, and unjust enrichment are all synonymous, because unjust enrichment is only one type of the broader category of quasi-contracts (contracts implied in law).
Contracts implied in law differ from contracts implied in fact in that contracts implied in law are not true contracts. Contracts implied in fact are ones that the parties involved presumably intended. In contracts implied in law, one party may have been completely unwilling to participate, as shown below, especially for an action in restitution. There has been no mutual assent, in other words, but public policy essentially requires a remedy.
Read more about this topic: United States Contract Law