Are you asking which words to use? Place? Or Down/Stay?
FWIW, I separate them. DOWN/STAY is formal obedience, does not last more that 5 mintues, unless the dog we are honouring in Rally is taking a long time, and it's fairly strict. The dog must not get up so high to switch sides that space can be seen under his belly or we'll be NQ'd. I want him to keep his focus on me.
I say MAT instead of place. Mat can be a variable length of time. It's not strict. My dog can stand, lie down, sit, wriggle around, have a scratch, as long as he stays on the mat. I can take anything resembling a mat with me, a towel say, put it down somewhere and tell him MAT. It will mean I want him to stay in that spot but he is free to move around within that spot as much as he likes. It is only kind to put the mat in a place out of the way of foot traffic, in someone else's home for instance, or in a place where the dog feels comfortable.