Question regarding apt purge and apt remove

[Kayjzjzk]

hello,
so i have tried removing packages using both apt purge and apt remove but i can still see some applications afterwards for example recently I installed lightdm using

sudo apt install lightdm

which i later uninstalled using

sudo apt purge lightdm

as well as

sudo apt remove lightdm

the output in terminal says that lightdm is not installed(after rerunning the above commands)

But i can sill see it in menu

And i can still open it(so its not just desktop icon)

So my question is why is this so? and what exactly is te function of the above two commands
additional info;
zorin os 16.2 core
i did setup lightdm as default login manger for some time
rightclicking on lightdm-->details-->remove in software center yields something along the lines "cannot remove package as it has unmet dependencies"

[Aravisian]

What you are seeing in app menu is not lightdm package, but a different Settings and Configuration manager tool for LightDM.
You can remove it with:

sudo apt remove --purge lightdm-gtk-greeter-settings

[Kayjzjzk]

Thanks a lot