Web fonts and desktop fonts
TTF and OTF are the formats your operating system installs. WOFF and WOFF2 are the same fonts wrapped in compression for delivery to browsers. Converting between them changes the packaging, not the design: outlines, hinting, kerning, ligatures and every OpenType feature survive unchanged.
WOFF2 is all a modern website needs. It uses Brotli compression plus glyph-specific transforms and is usually less than half the size of the original TTF. WOFF is only needed for very old browsers.
What we do not do
ConvertCove does not convert TrueType outlines into CFF outlines or vice versa, because that changes curves and hinting. When you unpack a WOFF2 file, the result is saved as .ttf or .otf according to the outlines it actually contains, and you are told if that differs from the format you selected.
Always check the font licence. Open-source fonts (SIL OFL, Apache) can be converted freely; many commercial licences restrict web or desktop use.