Why does the fan HA control card sometime show buttons and sometimes only a slider?



It might be the number of possible steps. I think up to 3 steps you get the discreet icons, >3 you get the continuous slider which kind of sucks. I wish it would go up to as up to 6 or even 8.
I’m going to try to find confirmation in the docs…

Because it depends on a particular fan entity. Check docs for a template fan to get an idea.

Thanks. Sure - but what property of the fan determines that :).
My theory is that it depends on the supported fan speed count.
Seems my fan which supprots 3 speeds shows the buttons but the 6-speed and 8-speed ones only shows a slider.