“Track” – to follow or pursue. You can track one’s progress and you could physically track them through the woods (follow).
To “trace” is to search by looking for surviving evidence. You can “trace” a picture by putting another piece of paper over that you want to copy and “trace” out the picture.
“Trace” can also apply to finding someone or thing: “I am trying to trace my long lost uncle” – you use past evidence to search him out (old addresses, old friends etc). The police might say “Put a trace on that license plate (use the computer records)”. When they “trace” who owns the car they can “track” him down.
And your explanation is fine, for example, you can “track” someone’s progress through school.
Track and trace are terms we use in business when we are concerned about packages we have shipped.
If I ship something by UPS (United Parcel Service) and I am concerned about its arrival. I can “track” its progress on line. The UPS website will give me real-time status of where my package is.
On the other hand, if I get a call from a customer saying that a package I sent via UPS has not arrived and it has been over a week, then I would ask UPS to trace this package. That is, they will look back over the tracking information and try to determine where the errant package is.