According to @Drew suggestion save-match-data give an all new match-data just as I wanted:

foo-bar-baz

(progn
  (save-match-data
    (goto-char (point-min))
    (re-search-forward "^foo-\\(.*\\)-baz" nil t)
    (message "step 1: %S" (match-string-no-properties 1))) 
;; => step 1 : "bar"

  (save-match-data
    (goto-char (point-min))
    (re-search-forward "^baz-\\(.*\\)-foo" nil t)
    (message "step 2: %S" (match-string-no-properties 1))) 
;; => step 2: no nil
  )