Are samatha and shamatha buddhist meditation the same thing?

all i can find is that samatha is theravadan and that shamatha in mahayanan, but not if they are just spelling variations or entirely different things

To start with, I've seen Samantha and Samandhi. And Samadhi Sutta, which interestingly discusses tranquillity and insight ( samatha and vipassana ).
There's another sutta which says that samatha and vipassana are paired qualities - samatha gets rid of passion, vipassana gets rid of delusion ( I'll see if I can find it ).  Note that samatha is a quality, not a method.