What is conjunctive truth table reduction?
In the binary case they are two of the seven truth-table reducibilities
$$m, btt(1), c, d, p, \ell, tt$$
based on polynomial clones.
See Figure 1 in Culver's paper
https://link.springer.com/article/10.1007/s00153-013-0351-x
for the classic diagram of the seven.

In the ternary case there are uncountably many such reducibilities instead of 7, as Culver demonstrates using a prior result about clones from universal algebra.