grammar - "It is me" vs. "It is I"?

Tonight I watched a movie (The Gospel of John) in which Jesus said (as quoted from the written Gospel of John), "It is I."

How does this expression differ from "It is me?"

Answer

This question about English pronoun case after copula (be) is a duplicate of Which is correct to say: "It's me" or "It's I"?, which links to a clear explanation.

Note that many answers on this page (such as Bill and Ham_and_Bacon) describe English pronoun case after conjunction (and), which is not necessarily the same as after copula (be).

To quote from the clear explanation:

The rule for what [Fowler] and others consider technically right is ... that "to be" should link two noun phrases of the same case, whether this be nominative or accusative. ...

Sometimes in English, though, "to be" does seem to have the
force of a transitive verb. ... The occurrence of "It's me", etc., is no doubt partly due to this perceived transitive force. ...

The final factor is the traditional use of Latin grammatical
concepts to teach English grammar.

To summarize the situation, It is me is the more commonly spoken form, while It is I is commonly written, taught in school, and sometimes spoken.