  In a first objective we improve our understanding about surjective and
bijective bounded linear operators preserving orthogonality from a
JB$^*$-algebra $\mathcal{A}$ into a JB$^*$-triple $E$. Among many other
conclusions, it is shown that a bounded linear bijection $T: \mathcal{A}\to E$
is orthogonality preserving if, and only if, it is biorthogonality preserving
if, and only if, it preserves zero-triple-products in both directions (i.e.,
$\{a,b,c\}=0 \Leftrightarrow \{T(a),T(b),T(c)\}=0$). In the second main result
we establish a complete characterization of all one-parameter groups of
orthogonality preserving operators on a JB$^*$-algebra.
