One patient will potentially have many (even hundreds) of encounters. Updates are always driven by the record of the resource itself - every resource (Patient, Encounter, Observation, CarePlan, etc.) has an 'id' element that represents the identifier of that resource on that particular server - sort of like a primary key. Updates are performed by making a RESTful PUT of the new record to a URL that includes that same identifier.
I.e. an update of an Encounter MUST always be performed with a URL of the form:
PUT [somebaseurl]/Encounter/[serverEncounterId]
The patient associated with the encounter will be referenced from within the Encounter object in the body of the RESTful call, but does not appear in the URL.