Fuuton Rasengan and Fuuton Rasenshuriken are two DIFFERENT jutsus

I just want to clarify this. I have been in an argument with some uninformed people who just refuse to listen. They say Fuuton: Rasengan is an incomplete version of Fuuton: Rasenshuriken.

In reality, it's never mentioned in the manga and anime fillers how Naruto created Fuuton: Rasenshuriken. I think the very reason people think Fuuton Rasengan and Fuuton Rasenshuriken are one because the only part of Naruto's chakra nature training shown was when he successfully created Fuuton: Rasengan. Then after a time skip, he entered the Team Kakashi vs Kakuzu fight and shows off his new Fuuton Rasenshuriken.

Since it's not specified that Fuuton Rasengan and Fuuton Rasenshuriken are one and Naruto specifically stated a different name for Fuuton Rasengan, we can safely assume that these two are different jutsus.

Theoretically, the effects of Rasenshuriken are supposedly very different from the effects of Rasengan:

Rasengan creates a very violent rotation backed up with force applied to chakra. Thus this creates a violent powerful ball of chakra that grinds whichever it goes in contact with. Hypothetically, adding the cutting effects of wind nature would just give rasengan added slice to its attack. Imagine being shredded by helicopter blades. If not, added wind nature would just simply increase the force of Rasengan giving it about 5x more power than nature-less Rasengan.

Now moving on to Rasenshuriken

Rasenshuriken has Rasengan as its base but Naruto, as hypothesized by Tsunade, adds millions (if not billions) of microblades through shape manipulation, those microblades are made of wind chakra. These microblades are the wind portion of the jutsu including four rotating "blades" that gives the jutsu its shuriken appearance. Applying the concept of Rasengan and Wind Chakra somehow makes the jutsu expand on contact, and the millions of microblades individually slice the enemy on cellular level - slicing every chakra tube connected to every cell and thus permanently preventing chakra usage on all affected cells.

As we can see Rasenshuriken and Rasengan have different effects, different appearance and different names. That's gonna be the very cue for every sensible person to consider the two jutsus different.