The Stanford Center for Internet and Society has a great summary of how the two cases differ:
In [Kahle v. Ashcroft], two archives [the Internet Archive and the Prelinger Archive] ask the U.S. District Court for the Northern District of California to hold that statutes that extended copyright terms unconditionally - the Copyright Renewal Act and the Copyright Term Extension Act (CTEA) - are unconstitutional under the Free Speech Clause of the First Amendment, and that the Copyright Renewal Act and CTEA together create an effectively perpetual term with respect to works first published after January 1, 1964 and before January 1, 1978, in violation of the Constitution's Limited Times and Promote...Progress Clauses.
Isn’t [Kahle v. Ashcroft] just Eldred v. Ashcroft all over again?
No... Eldred v. Ashcroft involved a challenge to the constitutionality of the Copyright Term Extension Act (CTEA), which extended the term of both existing and future copyrights by 20 years. In 2003, the Supreme Court rejected these challenges. Eldred focused narrowly on the constitutionality of the CTEA’s extension of the term of subsisting copyrights; the Court held that these extensions did not violate the First Amendment or the Progress Clause.