Final answer:
The differences between titling figures, text figures, hanging figures, lower-case figures, and old-style figures involve their design and use in typography, with each serving a specific purpose for text legibility and aesthetics.
Step-by-step explanation:
The differences between titling figures, text figures, hanging figures, lower-case figures, and old-style figures all pertain to typography and how numbers are represented within a text. Titling figures, also known as lining figures, are numerals that align with the uppercase letters and are used primarily for headlines and titles where consistency and emphasis are needed. Text figures, or old-style figures, resemble lowercase letters in their varying heights and alignments to provide a more blended flow within a block of text.
Text figures are traditionally used in body text where they do not distract from the flow of text. Hanging figures are a variant of old-style figures that hang below the baseline but still possess an irregular alignment that maintains the rhythm of traditional text. Lower-case figures are another term for old-style figures. Old-style figures are numerals that have ascenders and descenders like lowercase letters, which differentiate them from the consistent height of lining figures.