A WOFF2 downloaded from a website cannot be installed on most computers or opened in most design programs, because it is wrapped for the web. A TTF is the form every operating system installs. The wrapper is removed and the font itself is unchanged. Make sure the font's licence allows you to use it 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. WOFF2 is handled by a WebAssembly module that downloads the first time you open WOFF2 and is cached; the font is expanded back to plain tables. 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.