You should consider the a as a chaining symbol, separating the modifiers for the legs of a multi-leg move. So in afsafzafzW you see 3 a, which means the move has 4 legs. The modifiers for these legs are none, fs, fz and fz, respectively. So the first leg is a W move in all directions (no modifier). From there it continues forward-left or forward-right (because s = l or r), i.e. a diagonal step in the second leg. Then for the third leg it again deflects 45 degrees, but in the opposit direction as in the second leg, as this is what z means. Etc. So afsafzafzW is a shorthand for aflafraflWafraflafrW, two crooked trajectories that are each other's mirror image.
Haru's notation (afz)W is shorthand for WafzWafzafzWafzafzafzW..., a set of ever longer crooked trajectories. Every additional afz adds a new leg, which deflects in the opposite fl or fr (relative) direction as the previous leg did. (Which is the hallmark of a crooked move; if they would all deflect in the same direction, which you could do with fq, you would get a circular piece.)
The second leg in every sequence should really have been specified as fs, however, to indicate it can deflect in both directions, rather than only in one that is specified relative to the previous one. The first z or q occurring in such a sequence (i.e. before it is clear what 'opposit' or 'the same' direction means for the deflection, because there was no previous deflection) is always interpreted as s. You could see this as a special rule for expanding the parentheses into paths with different lengths.
You should consider the a as a chaining symbol, separating the modifiers for the legs of a multi-leg move. So in afsafzafzW you see 3 a, which means the move has 4 legs. The modifiers for these legs are none, fs, fz and fz, respectively. So the first leg is a W move in all directions (no modifier). From there it continues forward-left or forward-right (because s = l or r), i.e. a diagonal step in the second leg. Then for the third leg it again deflects 45 degrees, but in the opposit direction as in the second leg, as this is what z means. Etc. So afsafzafzW is a shorthand for aflafraflWafraflafrW, two crooked trajectories that are each other's mirror image.
Haru's notation (afz)W is shorthand for WafzWafzafzWafzafzafzW..., a set of ever longer crooked trajectories. Every additional afz adds a new leg, which deflects in the opposite fl or fr (relative) direction as the previous leg did. (Which is the hallmark of a crooked move; if they would all deflect in the same direction, which you could do with fq, you would get a circular piece.)
The second leg in every sequence should really have been specified as fs, however, to indicate it can deflect in both directions, rather than only in one that is specified relative to the previous one. The first z or q occurring in such a sequence (i.e. before it is clear what 'opposit' or 'the same' direction means for the deflection, because there was no previous deflection) is always interpreted as s. You could see this as a special rule for expanding the parentheses into paths with different lengths.