I am not OP so I can’t speak to this specific brand, but as a bit of a soda jerk; In general yes and no.

In the strictest traditions what is referred to as root beer in the west is (or was rather) made from the sassafras tree and sarsaparilla is made from a vine called smilax (or just sarsaparilla vine). However there are other ‘root beers’ like ginger beer and birch beer. Most sodas sold as root beer or sarsaparilla these days are made with or flavored to taste like birch or smilax as sassafras is carcinogenic and banned in some places.

While the other guy gives the deets about it, I can say in practice that sarsaparilla tasts like a dirty or unrefined root beer. This one in particular has something else I can’t place but it’s a really good sarsaparilla by tge standards of what I can get here.