apt-get (and apt-cache) is the classic interface, apt is the newer UI with the same functionality. aptitude is an old optional program that has a different resolver strategy, an optional full-screen UI and some other features. While some people use it for the additional features, others seem to think its resolver is better.
https://www.reddit.com/r/debian/comments/akmm4o/can_someone_explain_aptget_vs_apt_vs_aptitude_to/
https://www.reddit.com/r/debian/comments/9whj01/comment/e9q2bd2/?context=3
以前的草稿箱里的内容，现在使用apt，apt是apt-get的“升级版”，不仅可以进行.deb的软件包的安装，也可以下载镜像站中的包，不过.deb软件还是建议使用dpkg -i安装