You got part of it correct.
The rest of the story:
Contact tracing includes looking back for up to 14 days at who (and possibly where) the newly diagnosed patient (Suzie) was around. Those people should be contacted so they know they were possibly exposed & can isolate and monitor for symptoms.
If Suzie says, “Four days ago, Dan told me he had Covid.” They may ask: where were you? how long together? Was he coughing? Did you share food or drink? Did you touch the same things then touch your face?
Behind the scenes, data is being collected on how many newly diagnosed people had contact eith Dan.
As time has passed Health Agencies collect less information. The main focus is letting people know they’ve potentially been exposed.