`autoremove` is what you’re looking for: it removes automatically-installed packages which no longer have any dependencies. `apt autoremove` and `apt-get autoremove` are equivalent. `aptitude` doesn’t have an `autoremove` subcommand because it always removes such packages when they become candidates for removal ( _i.e._ auto-removable packages are removed along with the package whose removal causes them to become auto-removable).
Note that package installation and auto-removal isn’t symmetric in the default configuration; see How do recommends and suggests interact with apt-get dist-upgrade and apt-get autoremove? for details.
`clean` removes all downloaded `.deb` files from the package caches, and `autoclean` removes those which can no longer be downloaded. Both of these subcommands behave in the same way, with `apt`, `apt-get` and `aptitude`.