I would like to add to the discussion by first saying that I do not fully agree with the author on some things, while I completely agree on others. To begin I would like to discuss the things said by other members.
Shape manipulation and nature manipulation. These are the things that Yamato discussed as making up the various jutsu in the naruto world. Let us consider the shape manipulation. The rasengan, by nature of its name, are all round spiraling spheres. Because a sphere could be considered a perfect shape, it can be argued that the rasengan's form is at an apex of shape manipulation. In fact, besides the rasenshuriken variants which, despite a sphere in the middle, is primarily shuriken shaped (and thus rasenSHURIKEN as opposed to rasenGAN) all of them use the same form. As it stands, we have many rasengan technique variations, but only two form manipulations. Detractors can, and perhaps rightfully should use this as a reason to complain about lack of originality in the technique variations, whereas as fans can consider this an example of "don't correct what is not broken." In either case, when compared to the various shape manipulations displayed by other characters (I will use Sasuke due to their duality: spear, needles, dragon, hand-held disarray, body-wide disarray, sword) Naruto is lacking.
Next, I would like to discuss nature. This is where Naruto, conversely, improves his jutsu variation. He has infused..rather "completed" the rasengan with different natures. He has used wind, lava, magnetism, bijuudama plus minus chakra, and sage chakra. Here I will argue that the differently natured rasengan are different techniques. I will use two controls. First, the simple bunshin technique. We have seen MANY clone techniques (shadow, water, sand, lightning, ink, crow(?), earth, wood, mud, etc.) and they are all considered different techniques, despite all ending in '~bunshin' the same way Naruto's techniques end in '~rasengan.' But this may not be enough, since it can be argued that they all do the same thing (fool the enemy as to one's true position) so I will like to use my second control, which is the different effects of the natures. Let us consider the dragon bullet technique. There was a fire dragon bullet (Hiruzen), water dragon bullet (Zabuza), and earth dragon bullet (Hiruzen), and despite them all being of the dragon bullet shape (much like rasengan sphere shape) their effects are obviously different. So, using this as a base, we can consider the differently natured rasengan to be different jutsu from the basic version.
To conclude I would like to repeat that, while I do not agree that simply by shape manipulation some of the rasengan variations are different (rasengan, double rasengan, big sphere rasengan), the differently natured rasengan should be considered different jutsu. What do you think?