WOFF is TTF or OTF with compressed tables, built for browsers. To install a font from a website in your system or open it in a design program you need the uncompressed form. Check the licence before reusing a font outside the site it came from.
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 TTF can only be the matching kind. If the choice is wrong, the conversion stops and says whether OTF is the right one. A file that is not a TrueType, OpenType, WOFF, WOFF2 or collection font is refused.