Typography can look like lettering (Liza Pro, fancy OpenType fonts) but it’s not the same. It can even look like writing (formal scripts or handwriting fonts like FF Mister K), where the major parts of the letter or whole words are formed out of one stroke. In the same way lettering can look like typography (rub-down letters, fine rendering) or writing and still has nothing to do with those techniques.
The key nature of typography is that it makes use of prefabricated glyphs which are set according to abstract parameters. If you send a setting instructions like the following to someone at the other end of the world, he will be able to reproduce the exact same column of text, typographically, but never with one of the other methods.
Typographic parameters are font, size, leading, alignment (justified or ragged), tracking, kerning, line length like for example in:
ITC Garamond light, 14/18 pt, flush left, no hyphenation, tracking 0, line length 140 mm, paragraphs indented by 1 em.