KJV used Bomberg's Second Rabbinic Bible often called the Ben Chayyim text which was later published by Kittel as Biblia Hebraica Kittel (BHK) in 1906 and 1912. The NKJV used Biblia Hebraica Stuttgartensia (BHS), 1967/1977.
There are only about a half dozen differences that would affect translation.
No, they use the same Hebrew text. However, many of the differences between the KJV and later English versions (including the NKJV) is not due to differing Hebrew texts but rather to how they translated the ketiv-qere pairs. The KJV translators took each pair and evaluated it against all other evidence and made a decision that sometimes used the ketiv and sometimes used the qere. That has caused some to claim they were inconsistent, but I tend to think it was an attempt to critically examine every ketiv-qere pair rather than slavishly following every ketiv or every qere.
The NKJV translators did mainly use a different printed edition of the Hebrew text, but in those very few places where that edition differed from the 1525 edition edited by Ben Chayyim they followed the Ben Chayyim edition.
In effect, the NKJV is thus translated from the same Hebrew text as the KJV.
James D. Price, who was executive editor of the NKJV's Old Testament, wrote:
"For the New King James Version (NKJV), the Hebrew text of the Old Testament was the 1967/1977 Stuttgart edition of Biblia Hebraica.
Constant reference was made to the printed edition of the Hebrew Bible used by the translators of 1611, the second Bomberg edition edited by Jacob ben Chayyim.
In those few places where the Bomberg text differed from the Stuttgart edition, the Bomberg reading was followed" (King James Onlyism, p. 307).