etiquette: quote the points to which you're responding.

yes, the 98's & earlier can "shift hard".  later models of honda retard
ignition effectively "throttling back" when shifting up, like in f1
transmissions.  very smooth they are too.

yes, automatics have many clutches.  4-speed hondas have 4 main clutch
packs - 1 for each speed, together with a torque converter lock-up
clutch & 1-way clutch & other doo-dads for reverse.  there's all kinds
of stuff on the web about how automatics work, but most is for planetary
gearboxes, the most common sort.  hondas are different being essentially
a standard box with clutch packs instead of synchros - potentially more
efficient but less able to shift really high torque, [which should be a
non-issue with ignition retard or even "fly by wire"].

hard shifting is usually because non-honda transmission fluid has been
used.  are you certain it was dealer serviced with the correct fluid?
checked the service receipt?

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Yep, it's got clutches inside. I was suggesting you check your reciept
to see if they billed you for Honda Z1 tranny fluid. If you use anything
else (generally) they will shift like slamming a door . . . Wham.

'Curly'

Your throttle pressure cable might be a little tight.  It could make the
tranny think you are pressing harder on the accelerator than you really are.
Under light throttle pressure at what rpm is it shifting from 1st to 2nd and
from 2nd to 3rd?