A quick distinction:
Neoreaction (secular right, alt-right etc) focuses on social institutions - indeed, neoreaction regards institutions as primary.
Neoreactionaries say the problem with modernity is in the social institutions - (e.g. corruption by Leftism of The Cathedral of elite media, civil administration, educational organizations).
(Neoreaction regards religion as an institution, like any other.)
To fix modernity, the neoreactionaries say: first, fix the institutions.
They say: nothing good can happen unless we first fix the institutions.
They say: if (somehow, and that somehow is a major focus of discussion) we can fix the institutions - then things can, and probably will, improve.
Reactionaries (that is Religious Reactionaries) focus on religion.
Reactionaries say the problem of modernity is apostasy - the abandonment of religion.
We say: none of the above will happen without, first, religion.
Reactionaries say that religion is absolutely and unavoidably necessary (but not sufficient) to fix modernity.
Neoreaction disagrees because they see religion as an institution (just like any other) and corrupted by Leftism (just like any other), therefore: first fix the institutions.
Reaction regards religion as hierarchically-above other institutions, and something which cannot therefore be fixed by other institutions; but only by religion.
Reactionaries say: to fix the institutional basis of corrupt religion, we need real (not corrupt) religion, therefore: first, religion.