The arterty which supplies the oxygetated blood to your uterus has to work harder if you are laying on your right side. It ca be compressed if laying on your back. My yoga teacher has us all after 20 weeks laying on our left but before then on our backs for yoga nidra.
If you ever feel light headed or uncomfortable on your back or side, just change position.
I favour my right side when sleeping and have had no problems so far, if i am ever laying on my back i just wedge a pillow under one side so i am on a tilt.
Anyway - to answer your question - your yoga teacher is correct in saying that laying on your back and right side are similar