An escrow isn't a method, its more of an agreement. merriam webster defines the term escrow as
a deed, a bond, money, or a piece of property held in trust by a third party to be turned over to the grantee only upon fulfillment of a condition
So in the case of key escrows, you simply entrust your cryptographic keys to the key escrow provider to turn over to someone when a specific condition is fulfilled. In the case of a commercial key escrow, the condition is just that they confirm that the entity asking for the keys is authorized to access them. In case of a law enforcement key escrow, the condition would be that the LEOs have a valid warrant. Note that a key escrow by itself does not provide any protection. Protecting the keys is up to the key escrow provider.
An HSM on the other hand is a physical device that is designed to protect data (usually cryptographic keys). So, although a key escrow provider might be using an HSM to store escrowed keys, the two are fundamentally different things.