yes he knows more, he has summoning jutsu that uses hand seals, and he learned hand seals at the academy, simply for his fighting style he prefers to not have hand seals.....and the fact that he barely uses handseals is a feat of his power....the stronger the shinobi you are the less handseals you should have... ex tobirama being a super water style user used a jutsu with one handseal that took kakashi and zabuza 44 or so handseals to do......but before you get crazy over naruto not USING that many handseals, understand that handseals only exist to help focus chakra....so naruto couldve learned rasenshuriken quicker if he had tried to use handseals to focus his chakra to make the jutsu....but naruto became skilled enough to do it without handseals.....look at sasuke with chidori is a great example....at first he had to do a few handseals, but eventually he learned to do chidori and its variations without any handseals.... so simply naruto knows the handseals, but never uses them, and handseals arent really relevant.....the less handseals you use the better you are
Summoning uses four seals, one of which is the Ram Seal, used for Shadow Clones. He "learned" seals in the Academy, true. He also "learned" about chakra and "learned" about the Elemental Countries in general. Naruto learned basically nothing except some small practical aptitude in the Academy.
It's true that some of the most powerful ninja use few handseals, but some of the most powerful use MANY, and FAST. Itachi and Kakashi are examples here.
For Naruto's fighting style he "preferred" not to use many handseals during the Bell Test too, but that was because he legitimately COULDN'T use them. What has changed since then? Summoning Contract (Ignored after fighting Gaara), Rasenshruiken (Planetary Rasengan at some point), SM, KM, BM. ALL of the techniques used by Naruto in combat IGNORE handseals, even when he learned Fuuton and could presumably manage a Wind technique or two.
Handseals help gather and focus chakra INTERNALLY. "Knowing the handseals" for the Rasenshruiken wouldn't have helped because there WEREN'T ANY. And they wouldn't have helped if there were. Naruto didn't CHOOSE not to use handseals for the Rasengan, Rasenshruiken or similar techs; they arent handseal-based techniques. Like more or less EVERYTHING he USES, except Kage Bunshin. Is he compensating for some handicap?
That's an interesting thought. Naruto couldn't manage to learn Bunshin, so he learned Kage Bunshin.
Naruto couldn't manage to learn handseals, so he learned Rasengan, Rasenshruiken, Sage Mode, Kyuubi Mode and Bijuu Mode.
Of course, as he needs multiple versions of himself to manage Rasengan and Rasenshruiken, they don't really count as seal-less techniques...