The Trace-xDSCOperation cmdlet works on both local and remote target nodes and returns a collection of events related to a specified sequence ID. Typically, you will run Get-xDSCOperation and choose a specific sequence ID to run Trace-xDSCOperation against.
On the other hand, Get-xDSCOperation provides a general overview of what happened during a DSC operation and Trace-xDSCOperation provides specific detail. Most notable of these details is the message field, which reports the exact text or error reported by DSC when executing that operation.