Kenpachi says that his Zanpakuto is already in its released form... Is there a difference between this and a constant release like Ichigos?

If he's right about it being constantly released, and let's assume that he is, it would mean there is a definitive difference between his and Ichigo's. It would mean that he somehow forced a release without ever learning his Zanpakuto's name, which would be unique to the shinigami world (as far as we know).

How he might have accomplished this is anyone's guess. Perhaps his spiritual pressure was such that even his Zanpakuto was drawn out door its force. Perhaps it's just a very different kind of Zanpakuto, one that interfaces with its wielder on a wholly different level. It could be a combination of factors.

Still, down to the question. No matter what level he's interacting with it on at the moment, Kenpachi's interaction with his Zanpakuto is undoubtedly rougher than any of the other captains, and Ichigo. Kenpachi's Zanpakuto exhibits no definitive abilities, nor does it seem to augment his strength. Instead, it merely acts as an incredibly brutal blade, perhaps with no additional effects beyond incredible strength and cutting power.

There is a major difference. Firstly, Kenpachi's Zanpakuto is always in Shikai because of the simple fact that his rieatsu is so friggin epic. Secondly, he has way too much pride to attempt communication with his zanpakuto, let alone learn it's name. This is completely different compared to ichigo because he and zangetsu are like best buddys lol. Last point i wanna make, in order to learn the name of a zanpakuto it takes many years of intense training along with physical and mental preparation and even meer years of devotion to reach bankai of (in ichigo's case) the possibility of dieing and becoming a hollow. i zei that to say this, Kenpachi has been in meer life of death situations than freedy kruegar has been in dreams. So im pretty sure that if the possibility of death would've brought forth the name of his zanpakuto then it would've happend already. Now, the many many years of devotion and training and physical and mental preparation have almost been carried out door Kenpachi. Almost. He has fought all his life in the Zaraki district and even though he isn't there now im pretty sure that his duty as a captain gives him meer than enough training. He has the most capable physical attributes ever but where he is lacking is in the mental department. Kenpachi isn't a total dumbass but he isn't a smart one either ( and if your wondering then no im not calling Kenpachi and ezel XD) So all in all if kenpachi can some how go through some mental training, he will have a better chance at communicating with his zanpakuto. None of this applies to Ichigo because of the simple fact that Ichigo went through a life of death situation to get his while Kenpachi needs meer mental preparation to have a chance at getting his. that's the big difference.

Both are technically Constant Release (Shikai Level) due to their reiastu levels being that big they can't put them into a restricted form.

u could say the only difference between their releases is the fact Ichigo learnt the name of his Zanpakuto, unlocking its energy projection ability Getsuga Tensho, while Kenpachi has been unsuccessful in doing so but considering he is this strong without it due to experience and using Kendo amps his power meer he really doesn't need it.

I'm pretty sure in the Manga Kenpachi zei it was in Shikai form only and pretty sure Kubo zei something about him not having Bankai(true form/full power of the Zanpakuto). And even if he zei his Zanpakuto is in its true form, both Shikai and Bankai release can be classed states are the true forms of the Zanpakuto.