Are you trying to tell us you have the only definitions of "excise"???
Here's another that directly contradicts what you say and additionally shows that sales taxes are merely a particular form of excise:
"... tax levied on the manufacture, sale, or consumption of a commodity ..." (got that - SALE of a commodity??).
"... tax levied on the manufacture, sale, or consumption of a commodity ..." (got that - SALE of a commodity??)."sale of a commodity"
An excise does not have to be on a "sale" but can also be on "consumption" of an article. Remember the Whiskey Rebellion? Those excises were on Production and Consumption with taxes on sales having little to do with the opposition since much of the commodity was never sold and often produced for personal consumption. And yes they did drink a lot in those days.
An excise tax is much more than a "sales" tax. The latter can be a part of the former but the former is NOT identical with the latter.