Totally the variety. For super hoppy US beers I do prefer 1272 and Denny's favourite over US05 but only by a whisker of a beesdick's pubes. Not sure if I've used Bry97. I have an inkling I tried some when I couldn't get one of the others but my brain is vague.
For British or Belgians though - liquid variety and difference between each variety is noticeable with the same recipe. Coopers knockoffs would not work with anything but recultured or WL australian ale and I believe yeast strain is integral to kolsch (never made one, tasted and judged plenty) and alt (made many, love them). Only make one lager or so per year and only used dry for early extract versions so less qualified to comment but the few liquids I have used have had noticeable discriminating characteristics.
Never made the same lager twice so those discriminating characteristics have many variables but have done various brits many times over and the distinction there is very strong.
Also the difference between belgian saison, french saison and PC farmhouse is marked. never used Belle so not sure where it fits in.