The fact that was most likely discovered between the time of Mendeleev's table and the time of Moseley's table, which helped Moseley develop his version, is:
The number of protons in an atom is different than the atom’s total mass.
This discovery is significant because Moseley's work led to the understanding of atomic number as the defining property of an element, rather than atomic mass, which Mendeleev primarily used. Moseley determined that the properties of elements are better organized by their atomic number (the number of protons), which corrected inconsistencies in Mendeleev's periodic table that arose from the reliance on atomic mass.