A logotype is the company name set in distinctive lettering; a brand mark (symbol) is the graphic element; "logo" is the everyday umbrella term for the whole sign – symbol, logotype or their combination.
Designers use these terms precisely: a logotype is the typographic form (e.g. the word "Google"), a brand mark is the symbol (e.g. the bitten apple), and logo serves as the umbrella word.
Why does this matter practically? Because a good mark needs variants: horizontal, vertical, and symbol-only for small uses (favicon, app avatar). When we design a mark, we plan from the start how it behaves at 16 pixels and on a billboard.
Tip: if your company's mark doesn't work as a square app icon, it will cause constant problems in digital environments.