TinyTeX-0 contains the infraonly scheme of TeX Live, without any LaTeX packages. TinyTeX-1 contains enough LaTeX packages to compile R Markdown documents. TinyTeX contains even more LaTeX packages installed per request from the community. TinyTeX-2 contains the full TeX Live packages (created via tlmgr install scheme-full, and only exists in the daily release but not the monthly releases).
The zip packages are for Windows. The tgz packages are for macOS. The tar.gz packages are for Linux. Please see https://github.com/rstudio/tinytex-releases for more info.