What is TTF?
TrueType is the font format Apple designed and Microsoft adopted, and it is still what most desktop fonts are. Its outlines are quadratic curves, and its tables - glyphs, metrics, character maps - sit in a directory the file checksums against itself.
What is WOFF?
WOFF is a font wrapped for the web - the same TrueType or OpenType tables, each compressed, in a container browsers fetch happily. That is the whole format, which is why converting between WOFF and TTF or OTF is lossless repackaging rather than a redraw.