WOFF cannot be installed on most computers, and WOFF2 is smaller. OTF carries advanced typographic features and works in every design tool. WOFF is at home in fonts on web pages, as a fallback for WOFF2; OTF is the usual choice for professional typography with ligatures and alternates.
The outlines and tables of the font are copied unchanged and only the wrapper around them changes, so the letterforms, hinting and layout features are exactly the same. A web font holds either TrueType or PostScript (CFF) outlines, and OTF can only be the matching kind. If the choice is wrong, the conversion stops and says whether TTF is the right one. A file that is not a TrueType, OpenType, WOFF, WOFF2 or collection font is refused.