Does produced data fall under the "data collection" category?
There are probably many ways to think about this, but in the statistical world view I think the word you are looking for is dependent variable. 

Statistician see students (or any other object for that matter) as a stochastic process that produce outcomes (dependent variables) given traits that we can observe (independent variables). 

Data scientists tend to call those things target outcomes and features respectively. 

None of these terms however mean anything about who owns the data. Philosophically a dependent variable is produced by the stochastic process (the outcome is governed by the givens), and are in a sense a characteristic of the process. Policywise this doesn't carry much weight though. GDPR for instance is mainly concerned about data that can be used to identify persons. That isn't likely the case with outcome variables, but it can be!