While the Kage Bunshin no Jutsu seems to be taught, the Tajuu Kage Bunshin no Jutsu is sealed, so nobody can learn the jutsu.
Weeeeellll... not quite! The Naruto Wikia seems to be a bit off on this bit, since the technique that was sealed away was actually the "regular" Kage Bunshin no Jutsu — the technique that's taught is actually the Bunshin no Jutsu.
Or why was the Tajū Kage Bunshin no Jutsu sealed away?
The Kage Bunshin no Jutsu is a forbidden jutsu, and that was why it was sealed. Since its "massive version," the Tajuu Kage Bunshin no Jutsu, is just a variation of the same technique, it was also sealed away.
It is forbidden because of the danger it present to its user, since it distributes an equal amount of chakra between all the clones that comes directly from him. This could easily drain the total amount of chakra from a user who has less control over it.
Does that mean that there's a difference between these jutsus, aside from the number of Kage Bunshin created?
If there's no other difference, everybody could use this without reading the sealed scroll.
As for differences between it and the normal technique, I'd say that the amount of chakra necessary would be its main difference in terms of execution — the more chakra you have, the more clones you can generate.
However, most people won't use the "massive version" of the jutsu simply because of the danger mentioned in the above section — not many shinobi can use such high amounts of chakra and safely maintain the technique steady.
Adding "Tajuu" in front of it is just something that Naruto does every once in a while (note that he sometimes generates huge amounts of clones even without saying "Tajuu") when he intends to generate a massive amount of clones instead of a "regular" one. You can double check this in the very first chapter, where Naruto reads the scroll and never makes mention of the "massive version" of the technique.