Yes sometimes milkshakes are called frappes, possible French origin.
But usually soda is called soda , afaik.
But Moxie was called a tonic.
And grinders are still call subs in many parts of NE.
If you want to make a malted milkshake you could try adding Ovaltine if you can find it. Ovaltine used have high malt content.
Way back in the sixties, I was on vacation with Mom and Dad and we camped outside a very small town; the theater had closed but they still had drug store soda counter.
I ordered a chocolate and and was amazed and thrilled when it was made with chocolat ice cream and chocolate milk.
Ovaltine's name from its home country, Switzerland, is -- OVOLMALTINE -- is made with maltextract; later on came Ovaltine with Cocoa added.
Nestle's bought the rite to U.S. production.
Finding the original is now harder than getting the cocoa flavored version.
Back in the early oughts, when shipping prices were low, I ordered a case of Moxie from an online place that carred soda's not available nationwide normally.
It was different; I ordered from them for several years till shipping became asininely high.
Bought one case with 24 different root beers; now I can go to two specialty stores in the Twin Cities and get probably 70-80 percent of the sodas made in the U.S. and a good number from other countries.
I drank a lot of Ovaltine when I was in grade school, both types.