Mintty isn't an alternative to Cygwin, it's a part of Cygwin: an alternative to the standard windows terminal that Cygwin used to launch by default. Recent Cygwin installers actually set up Mintty by default.
You seem to be confusing terminals (programs that provide a text environment) and shells (usually text-based, often run inside a terminal). Mintty is a terminal. cmd.exe is a shell, but will spawn Windows' own ANSI terminal when asked. Cygwin's bash will also spawn Windows' own terminal when run without one. Fish is a shell, and needs to be run inside a terminal.
Console2 is different again. As I understand it, it wraps Windows' terminal, providing some extra features.
You seem to be confusing terminals (programs that provide a text environment) and shells (usually text-based, often run inside a terminal). Mintty is a terminal. cmd.exe is a shell, but will spawn Windows' own ANSI terminal when asked. Cygwin's bash will also spawn Windows' own terminal when run without one. Fish is a shell, and needs to be run inside a terminal.
Console2 is different again. As I understand it, it wraps Windows' terminal, providing some extra features.