Seifer's injury may have been less severe, more superficial than Squall's. After all, Squall was already wounded when he struck back.
Seifer probably just got a couple of Curagas cast on himself then went along his merry way... whereas Squall's wound might've needed a combination of magic and physical treatment.
I'm pretty sure there was some curative magic involved, since both characters are unbandaged within hours of getting cut, and neither of their injuries re-opens during the stress of battle that same evening.