Jefferson's Wall of Separation

Consider Prof. Dreisbach"s reserach on Jefferson's Wall:

Throughout his public career, including two terms
as President, Jefferson pursued policies incompatible
with the “high and impregnable” wall the modern
Supreme Court has erroneously attributed to him. For
example, he endorsed the use of federal funds to build
churches and to support Christian missionaries working
among the Indians. The absurd conclusion that
countless courts and commentators would have us
reach is that Jefferson routinely pursued policies that
violated his own “wall of separation.”
Jefferson’s wall, as a matter of federalism, was erected
between the national and state governments on matters
pertaining to religion and not, more generally, between
the church and all civil government. In other words, Jefferson
placed the federal government on one side of his
wall and state governments and churches on the other.
The wall’s primary function was to delineate the constitutional
jurisdictions of the national and state governments,
respectively, on religious concerns, such as setting
aside days in the public calendar for prayer, fasting, and
thanksgiving....
Jefferson’s refusal, as President, to set aside days
in the public calendar for religious observances contrasted
with his actions in Virginia where, in the late
1770s, he framed “A Bill for Appointing Days of Public
Fasting and Thanksgiving” and, as governor in 1779,
designated a day for “publick and solemn thanksgiving
and prayer to Almighty God.”
How can Jefferson’s public record on religious proclamations
in Virginia be reconciled with the stance he
took as President of the United States? The answer, I
believe, is found in the principle of federalism. Jefferson
firmly believed that the First Amendment, with
its metaphoric “wall of separation,” prohibited religious
establishments by the federal government only.
Addressing the same topic of religious proclamations,
Jefferson elsewhere relied on the Tenth Amendment,
arguing that because “no power to prescribe any reli-
gious exercise…has been delegated to the General [i.e.,
federal] Government[,] it must then rest with the States,
as far as it can be in any human authority.” He sounded
the same theme in his Second Inaugural Address,
delivered in March 1805:

"In matters of religion, I have considered that its
free exercise is placed by the constitution independent
of the powers of the general [i.e., federal]
government. I have therefore undertaken, on
no occasion, to prescribe the religious exercises
suited to it; but have left them, as the constitution
found them, under the direction and discipline
of State or Church authorities acknowledged by
the several religious societies."

These two statements were, in essence, Jefferson’s
own commentary on the Danbury letter, insofar as
they grappled with identical issues. Thus, as a matter
of federalism, he thought it inappropriate for the
nation’s chief executive to proclaim days for religious
observance; however, he acknowledged the authority of
state officials to issue religious proclamations. In short,
Jefferson’s “wall” was erected between the federal and
state governments on matters pertaining to religion.

 How does Justice Black's wall in Everson differ from Jefferson's wall?