Acetic acid or ethanoic acid - trivial names vs systematic names and correct formula representation
While I agree that the systematic name ethanoic acid makes a lot more sense, the name acetic acid has been used for so long that it's the accepted IUPAC name and is used almost universally. Both refer to the same compound.

Molecular formulas like $\ce{C2H4O2}$ are often seen when doing elemental analysis and the like, but give no structural information. $\ce{CH3COOH}$ makes it clear that it's an acid and shows the carbonyl group.