zsh で、PATHを追加するときに大文字のPATHと小文字のpathとで挙動が違った

https://unix.stackexchange.com/questions/532148/what-is-the-difference-between-path-and-path-lowercase-versus-uppercase-with

$PATH はstringで、$path$PATH に紐付けられた配列ということらしい

$ echo $PATH
/opt/homebrew/bin:/opt/homebrew/sbin:/usr/local/bin:/usr/bin:/bin:/usr/sbin:/sbin
 
$ echo $path
/opt/homebrew/bin /opt/homebrew/sbin /usr/local/bin /usr/bin /bin /usr/sbin /sbin
 
$ typeset -p path
typeset -aT PATH path=( /opt/homebrew/bin /opt/homebrew/sbin /usr/local/bin /usr/bin /bin /usr/sbin /sbin)