A contractor requests completion, you confirm it. Where their write-up goes.
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When a contractor finishes, they request completion from their link. That is a request, not a decision: the work moves to waiting on you, the managers are told, and you confirm it. Nothing is marked done on the contractor's say-so alone.
Technician notes are the contractor's own write-up of what they did. They post to the ticket, so the account of the work lives with the work rather than in somebody's email. They can be written while the job is running as well as at the point of finishing.
Both actions are limited to the contractor who was actually awarded the job. A contractor whose bid was turned down cannot request completion or write notes, even from their original link.