Yes and no... I do agree that Bellingham glides more, but both can/could play any position in the center of the pitch on a high level and score lots of crucial goals. How they do it does indeed not look the same, but still I think he is a closer comparison than Zidane for example, who didn't have the physical power and versatility Ballack and Bellingham have, but who played with more technical ability and elegance.
The cross-reference with Ballack is in them both being eclectic, but Ballack's area of effectiveness or, I guess desire to play in is smaller than Bellingham's - Bellingham looks like he can convert any kind of chance in any kind of way required, and I'm not saying that exaggeratively as he has the mix of street football, finesse and athleticism plus the aforementioned power to have a massive array of finishes and assists. Someone compared him to Gullit in this sense further up the page and I think what's happening is everyone is recognising that this kid has a smorgasbord of finishes and accents to his game. Ballack wasn't like that; he'd power in a header, he could take shots on, but his range wasn't so vast. I'm not saying it as an insult either. Ballack, like Gullit, was, to this point in Jude's career, far, far better in the air, too, and a lot more probing plays were sent his way aerially - both Gullit and Ballack were absolutely dominant in the air and also in terms of positioning to receive the header. Madrid don't send crosses of that nature in much, to definitively know if Bellingham has that level in him, but to this point in time, there's no evidence to say that he has.
He ghosted a little, but most times met the ball with power and strength - opponents could see exactly where he was and what was about to happen, but could do nothing to stop him. I'm not saying he was all brute force because that wouldn't sound or be right, but he wasn't able to initiate a chain, be connective in it, suddenly disappear from it only to appear on the other side of the pitch to finish it off, apparently unbeknownst to those around him.
I think on one of those octagonal attribute markers, Ballack's would be more attenuated than Belligham's - in other words, Bellingham can do more and make it look seamless than Ballack, but on one of those marker things, Ballack's heading would be top percentile where as Bellingham's would currently sit at least two gradations less, so if we're saying out of a 100, Ballack's is at least a 90 and Bellingham's is in the 70's somewhere, I'd say Ballack was also outright stronger than Bellingham will perhaps ever be, but after that, I don't think there's an attribute he has over the kid. I think they both played to the remit of their physical gifts, too, but Bellingham has been blessed with more in that regard: more agile; better dribbler; a lot faster; quicker combination player; more mobile; more able to use his length because of his agility(if that makes sense - the amount of times he does that Haaland, stretchy thing of extended toe poke passes and shots others can't reach is becoming a trademark). It's hard to say one is more intelligent that the other because that's just about application and the ability to affect play and both have that in bucketloads.
What will also be telling is in how long Bellingham plays like he is doing. 'Leverkusen Ballack' was rather short lived when we consider his career as he never got near those heights at Chelsea and so we have the nearly-treble winner version of him to go by and then a slide as that level wasn't maintained.