In addition to nice gaijin-san's explanation, there are cases where those two expressions are interchangeable. For example, にございます can work as a classical version of です.
殿:あそこにおるのは誰じゃ。
部下: 佐助にございます。(=佐助でございます。/佐助です。)
Lord: Who is that?
Subordinate: He is Sasuke.