why do some people think sarsaparilla and root beer are the same thing?

They do taste similar but I can tell the difference.

Both beverages are named after their distinct differences in ingredients when they were first made. Sarsaparilla was made from the Sarsaparilla vine, while Root Beer, roots of the sassafras tree. These days, Root Beer recipes do not include sassafras as the plant has been found to cause serious health issues.

ignorance of  awareness  of the basic     history

SARSAPARILLA ( root )  aka Smilax omata is a perennial  trailing vine with prickly stems native to Mexico and Central America  the Beverage  ( soft drink ) produced   it does have a SIMILAR FLAVOR to ROOT BEER 

Sarsaparilla WAS  popular  in the United States in the 19th century   promoted  in ads as cures for patent medicines  from skin to blood problems  CLASSIC U.S> sarsaparilla the drink  was NOT  MADE from extract  of the sarsaparilla PLANT  but rather  originally made from a BLEND of  BIRCH OIL and  SASSAFRAS the dried  ROOT BARK of the SASSAFRAS TREE  COCA COLA  first marketed  the drink  in 1885 as a remedy for HANG OVERS headaches and MORPHINE ADDITIONS

in 1960 the FDA  banned the use of  SASSAFRAS OILS in food stuff after evidence of accumulation the main constituent SAFROLE  was CARCINOGENIC  Safrole is also found in nutmeg mace cinnamon arise  black pepper and sweet Basil in  low concentrations of safety

  ROOT BEER and BIRCH BEER  ROOT BEER is a SWEET North American beverage  made traditionally  using the  ROOT BARK  of the SASSAFRAS TREE Sassafras Alibidium ( note NOT   SIMILAX OMATA )  now containing ARTIFICIAL  sassafras by  A & W Barg's Dad's Hire's and Mug   since  banned as a carcinogen 

Actually sarsaparilla and cream soda are the same thing.

To piss you off.

Because they are very similar .. at least in the US during the 1800's.

Real root beer is nothing like the soda pop. And it is usually fermented so it often IS an alcoholic drink.  Some root beer is made from sarsaparilla roots (this is a vine).. other versions are made from the root bark of the sassafras tree (you pick saplings, not full-grown trees).

I lived in south-eastern Pennsylvania near Amish areas, in the 1950's and 1960's, and their cheeses, breads, and root beer were very tasty.  I suspect Amish root beer was made from sassafras roots, only because I know that sassafras grew in the woods behind my house .. .don't know if Smilax ornata vines (sarsaparilla) grew locally.  The leaves of sassafras trees are very distinctive, and as a child I loved how some of them looked like little mittens.

I'm guessing that most people are like me - they don't really give a lot of thought to root beer or sasparilla, a lot of them not even knowing what the second one is. I guess some of them just guess they're the same.

Because most folks have not a clue what sasparilla actually is