Why would a smaller AIC than BIC lead to an increased chance of both overfitting and underfitting? I am puzzled by the following statement in my lecture notes

AIC penalty smaller than BIC; increased chance of overfitting 
BIC penalty bigger than AIC; increased chance of underfitting

Is there a typo?

A stronger penalty will reduce the size of the fitted model.
A weaker penalty will increase increase the size of the fitted model.

AIC penalty smaller than BIC; increased chance of overfitting
BIC penalty bigger than AIC; increased chance of underfitting

The AIC penalty is smaller*, this will increase the size of the fitted model. As a consequence, the use of AIC increases the probability of overfitting in comparison to the use of the BIC.
The BIC penalty is larger*, this will decrease the size of the fitted model. As a consequence, the use of BIC increases the probability of underfitting in comparison to the use of the AIC.


*

*(if the number of observations is larger than 7)

