Lactase tablet vs. lactose-free milk question

I am wondering if there is a principle difference between taking a Lactase pill and then drinking normal milk as compared to drinking lactose-free milk?

I have been drinking the latter, but it occurred that if these were interchangeable, it would be much cheaper to just take the pill and drink normal milk (as the delta between the price of normal and special milk is very large in my country). On the other hand, if there is even a small amount of downside in health I would rather spend the extra money.

I appreciate that this may be a rudimentary question, as it stems from my ignorance of how the Lactase pills actually work; I thank you for your time in answering my post!