Is there a difference between Mazda’s skyactive turbo engine and other automakers turbo engines?
Not really. It's all marketing. SkyActive, EcoBoost, Earth Dreams....really just branding for the manufacturers to use on their most fuel efficient engines.
There is some difference in how the Mazda engine emphasizes low-end torque over high-RPM horsepower (they basically speed up airflow at low RPM). It is a little more than marketing as the whole vehicle was designed in a holistic manner (i.e. transmission with aggressive lock-up converter paired to complement characteristics of that super high-compression engine) and I wouldn't say it's just marketing hot-air. For that, look to the troubles Boeing got into by putting lipstick on a pig (i.e. 60's design of 737 with new high-bypass engines that aren't a good fit for that architecture; changing architecture, i.e. raising ground clearance is prohibitively expensive).
Incidentally, I read yesterday that Boeing won't be using the MAX name any longer for their "redesigned" 737s:
I'm sure renaming RMS Titanic to, say, RMS Brittle Rivets would have saved that ship too 😉
https://www.automobilemag.com/news/deep-dive-inside-the-mazda-skyactiv-2-5t-turbo-engine
https://www.motor1.com/news/223763/mazda-skyactiv-x-technology-explanation
I must say, given the troubles Honda has had with small displacement engine turbos ( https://www.youtube.com/watch?v=VIRBsn3xfoc ), Mazda's decision was the right one. Others seem to be following suit with Hyundai just putting out a 2.5L I4 turbo in their new $56K Luxury sedan. The Inline 6 that Mazda is developing for sharing with Lexus in 2 years is also a smart bet following the path blazed by the M256 Inline 6 Mercedes engine.