Yes, the name is confusing but they are now the "standard" way to deal with Unicode in both Delphi and Lazarus.
However the functions without Ansi... are reserved for dummy ASCII compatible compare without locale or sorting info.See: http://docwiki.embarcadero.com/Libraries/Berlin/en/System.SysUtils.CompareStr http://docwiki.embarcadero.com/Libraries/Berlin/en/System.SysUtils.AnsiCompareStrIt is a historical remain I guess.
BTW, I was reading about the new Delphi compiler for Linux. They had made big changes for string types.