Algebraically equivalent clones

Two functional clones $F$ and $G$ on a set $A$ are said to be algebraically equivalent if sets of solutions for $F$- and $G$-equations coincide on $A$. It is proved that pairwise algebraically nonequivalent existentially additive clones on finite sets $A$ are finite in number. We come up with results on the structure of algebraic equivalence classes, including an equationally additive clone, in the lattices of all clones on finite sets.