I'd argue that they pretty clearly are different, if you're talking about generic laziness-as-a-quality versus subject specific laziness.

Someone who isn't interested in school might be willing to work very hard at improving in a sport, or work very hard on their extracurricular club, or work very hard to teach themselves assembly and programming, or to learn a musical instrument. They might even be willing to work hard to teach themselves math, but be uninterested in putting effort into math class.

I guess it depends on if you consider "laziness" a universal character quality or not.

Despite having agreed with you above, I'd agree with the dissenting post here as well, that while not caring about something can lead to being lazy regarding it, they are not intrinsically the same thing. I care about my house, but I'm still lazy about getting on the roof and cleaning the gutters. I don't care about many of the jobs I've held in the past, but have still done the day to day work to the best of my ability because professionalism. If we're looking deeply at psychological cause and effect, there may be some utility to examining whether the outcome roots in one or the other. (for me it was both)