Below is a comparison of the numbers in two serif faces, Times New Roman ("TNR") and Constantia:
The full-height numbers are called lining numbers, and the variable-height numbers are called old oldstyle figures. In the years shown on the coins below, the American penny used oldstyle figures and the Canadian penny had lining numbers.
The advantage of oldstyle figures is that they don’t POP OUT from the text like uppercase letters, but instead blend in with the words. Strangely, the digits 6 and 8 are the same height in both systems, so “6668886868” would pop out just as much in TNR as in Constantia.
If you are using a face with oldstyle figures in text, you can have a problem if you have a reference to a zero (o) which looks just like the letter “o.” Temporarily switch to another face with a full-height zero.
Some “expert set” type packages for faces that normally use oldstyle numbers also include lining numbers to provide extra design freedom.