It's both: Fate Core is its own system, and it's also one that's an update/revision to the Fate mechanics. In Evil Hat's Fate Core kickstarter, they write:
Today, Evil Hat is proud to bring you Fate Core: the latest evolution of the Fate role-playing game system. Inside you'll find refined, clearer language about every part of the game -- ranging from streamlined language about aspects and skills, to a unified approach for game actions and outcomes, to our trademark, rock solid GM and player advice.
Simply put, Fate Core is the best version of Fate we can possibly make, built upon over a decade of play and design experience by Evil Hat, and with the Fate player community at large, taking the best lessons from all of gaming and distilling them into a cohesive, compelling whole.
Emphasis is theirs.
Fate Core includes a Veteran's Guide section which describes itself as “a guide to the major changes to the system from previous versions like Spirit of the Century and The Dresden Files Roleplaying Game.” The veteran's guide itself also describes Fate Core as “a new version of Fate [developed to] update and streamline the system.”
(The Fate SRD site I linked to is a free and comprehensive reproduction of the Fate Core text, plus enhancements, thanks to the whole of Fate Core being available under CC-BY. It's not a subset of the book text, it's the whole book text.)
Now, whether Fate Core is an improvement to you, and whether it works well for you, is subjective. The authors at Evil Hat believe it's a genuine improvement over earlier editions and that it achieves more effectively the same objectives they were always striving for: in this iteration summarised as being about proactive, competent characters leading dramatic lives. It isn't some tangential unrelated edition and it isn't trying to achieve unrelated goals; it's definitely an update. I'm conscious there's some communication mistakes they made in previous editions they took care to correct in Fate Core, like how a passage in Dresden Files RPG was read by many people as implying that aspects weren't Always True (they are, and they were intended to be).
The old editions are still available and playable though, and they may work better for you or your group. Go ahead and use them; you're not obligated to play Fate Core specifically. Other people may recommend you use Fate Core because they never played older editions or they genuinely think it's a major improvement — I can't really answer what motivated people to say the things they did.
It's worth bearing in mind that right now, true to its name, Fate Core was intended to be the core of new offshoot iterations of the game, such as the pay-what-you-want-including-free Worlds of Adventure for Fate Core. (The Worlds of Adventure are funded via a patreon; anything else on top is just goodwill from buyers.) Games like Atomic Robo RPG (not free) or Masters of Umdaar (one of the Worlds of Adventure) have taken that and run wild with their own improvements which will probably be collected back into a Fate Core 2 at some point. My own group has taken a lot of lessons from all the variants we've played, and either play with one of them as a base, or play with the Core or Accelerated edition modified by what we think will work best. (Accelerated is just a stripped-down simplified version of Core.)
