I ran into this same question when I first got my spa. On paper, chlorine is chlorine, but I learned there’s a bit more to it than that. The spa stuff is generally made to dissolve quickly and at lower doses, which works better in the smaller volume and higher heat of a hot tub. Pool chlorine can work, but I found it’s way easier to overshoot the levels, and then you’re stuck waiting for them to come back down before you can soak.
I actually tried using some leftover pool granules once, seemed fine at first, but the next morning the water felt harsher and my skin was a bit itchy. It could’ve been a coincidence, but that was enough to convince me to stick with spa-specific chlorine most of the time.
The other difference I noticed is stabilisers. Pool chlorine often has more of them to protect against sunlight, but in a covered spa, they just build up and can make balancing harder. If I’m ever in a pinch, I’ll use pool chlorine very carefully and in smaller amounts, but day-to-day, I find the hot tub version keeps things simpler.