I would be shocked if the difference between BAW56 and BAV23A mattered. Maybe it's one of those applications, maybe you can give some context as to whether it would matter, but I would most likely think it doesn't.
Notable differences seem to be V_R, t_rr, C_d (a little bit, but their tolerances easily overlap), and maybe I_FSM (curiously, both provide a plot of this vs. t_p, but onsemi erroneously rates it at 4A (1µs) while plotting 11A!). It would be weird if V_R is being used as a characteristic (avalanche, but the voltage doesn't matter?*), but again, there's an outside chance it could matter.
*In that they're not rated for it, as zeners are; or avalanche rectifiers for that matter. So the actual voltage is anyone's guess. Usually it's 10-40% above V_R, but it could be many times higher as is often the case with rectifiers (I have name-brand 1N4004s that break down ~1.3kV). They will still avalanche, most likely nondestructively at low currents (DC, thermally limited; pulsed may still be destructive), but the V(I) curve and tempco will be all over the place. That's generally the case for rectifiers, anyway; I haven't tested a whole lot of small-signal diodes in breakdown.
Tim