There are two things going on: one is the script, and the other is orthography.
The classical orthographic system uses consonantal "u" and "i" -- both are used for both the vowel and the consonant. A later orthographic system uses "v" and "j" when "u" or "i" are used as consonants. Today, you'll find a dog's breakfast of orthographic systems, sometimes in the same text (e.g. some current texts use consonantal "u", but do not use consonantal "j" and strikes some people as barbarically inconsistent).
In the classical world, you had engraving and handwriting. Handwriting was done in a Roman cursive script and looks quite different than anything you've probably seen. Engraving was done in majascules and written "U" looked like "V", just to totally confuse everyone after the middle ages (and because V is probably easier to engrave than U).
The classical orthographic system uses consonantal "u" and "i" -- both are used for both the vowel and the consonant. A later orthographic system uses "v" and "j" when "u" or "i" are used as consonants. Today, you'll find a dog's breakfast of orthographic systems, sometimes in the same text (e.g. some current texts use consonantal "u", but do not use consonantal "j" and strikes some people as barbarically inconsistent).
In the classical world, you had engraving and handwriting. Handwriting was done in a Roman cursive script and looks quite different than anything you've probably seen. Engraving was done in majascules and written "U" looked like "V", just to totally confuse everyone after the middle ages (and because V is probably easier to engrave than U).