When I tell someone:
do they need to be standing at that moment? When I tell someone:
do they need to be sitting at that moment?
If yes, is there a more general statement (edit: preferably including the word "still") that can include both?
Edit: I probably should have given a better context to my query. I am thinking of a situation when you tell someone to stand/ sit still, so you can do something:
Stand/sit still or I will pierce you instead of your shirt with this pin!
Does the reader guess from that the position the person spoken to is in?
Yes. If you tell someone to stand/sit still they do need to be standing/sitting at that moment.
"Keep still" and "Don’t move!" are commonly-used commands that include any position they may be in.