A bit of both actually.
Strands of Fate is a big giant toolbox right? It has default rule systems, but usually offers one or more alternatives. The stress track is a good example of this. It offers one set of stress rules as the default, but then provides two more that can be used instead.
Nova Praxis used some of these variant systems, and as it happened, many of the ones that best worked for the setting were those that more closely matched the "classic" FATE rules. Again, the stress tracks are a good example of this. So are Skills. The versions of the stress track and Skills rules we used in Nova Praxis are in Strands as optional rules, and are very similar to those found in other FATE games.
And yet, some things came straight from Strands. Nova Praxis still uses the Aspect Alphabet, Persistent Aspects, and a few other bits that are uniquely Strands.
Then along came FATE Core, which introduced some new ideas that worked well with Nova Praxis. So, that being the case, we made some tweaks to NP specifically designed to adopt the changes we likes and to make it easier for someone who likes FATE Core to hop right into Nova Praxis (especially in terms of how Aspects are used). In some cases we were limited in how compatible we could make it with FATE Core because Evil Hat hadn't released the OGL for it yet. That's why, in many cases you'll notice that NP functions the same way as FATE Core mechanically, even if the terminology is a little different.
In other cases, the FATE Core rules didn't properly reflect what we were trying to do with the setting. And that was the biggy. The rules had to reflect the setting. Compatibility with any other rule set always took a back seat to that.
So there you have it.
The rules for Nova Praxis are sort of a Strands of Fate/FATE Core hybrid, with a number of tweaks or new elements added in to make it work for the setting.