The paper you cited is dated 1960 and bears McCarthy's name.

The Lisp 1 Programmer's Manual is dated 1960 and ... bears McCarthy's name.

The paper you cited has a section titled The LISP Programming System which says:

"The LISP programming system is a system for using the IBM 704 computer to compute with symbolic information in the form of S-expressions."

The Programmer's Manual's Preface begins:

"LISP 1 is a programming system for the IBM 704 for computing with symbolic expressions."

Looks like they are about exactly the same thing to me: an implementation for a specific computer (IBM 704), described in the same year by the same author, with an a nearly identical sentence in the intro.