My understanding is that:
1) The target value of each leaf in a Regression Tree is calculated as the mean of the target values of the instances that reached that leaf during training.
2) The value of each leaf in a Model Tree is a linear function using a subset of the features, determined by performing a linear regression of the instances that reached that leaf during training.
Is the tree.DecisionTreeRegressor in scikit-learn a Regression Tree or a Model Tree?
You're understanding is right. Mathematically, a regression tree represents a piecewise constant function, while a (linear) model tree is a piecewise linear function.
DecisionTreeRegressor is a regression tree.