Dogs definitely understand words in a way that cats don’t. (Or don’t let us know about.)
River will go out in the morning and relieve himself along the sidewalk by the house. He will turn to go back inside. But if I say “paper” (aka “newspaper”) he knows we are going up to the road.
I say “paper” to get the mail as well. I don’t want to confuse him with too much technical detail.
If he were truly your dog he would have corrected you on that technical detail.