THat's a good question. In French we say "les impôts" to talk globally, and then we have different kinds of "taxes" like "l'impôt sur le revenu" which is something you pay from your salary. But I really don't know if there's such a word in english. Sorry I can't answer, but I hope someone will.
The big one in U.S. English is "income tax" (l'impôt sur le revenu), although I notice that "payer des impôts" refers to income tax without a more specific reference. http://www.larousse.com/en/dictionaries/french-english/imp%C3%B4t/41879 It seems the only way to refer to a specific tax is to include that reference, i.e., "Nous devons payer l'impôt de vente" (We have to pay sales tax). Is that right? Is there a difference between "l'impôt" and "la taxe"?
Technically, there is a difference between "sales tax" and a "VAT."
A "sales tax" is a one time tax for which the consumer is wholly responsible.
A "VAT" is a tax payed on the value added at each level of the production/supply chain.
From the consumer's standpoint I think the effect is similar as the VAT tends to trickle down the supply chain to the consumer.
So ultimately, I would probably say that US "sales tax" translates to "la taxe de vente," whereas UK "VAT" tanslates to "TVA." In the grand scheme of things, the semantic differences probably don't amount to much.
Also, am I correct in assuming that "un impôt" refers to a tax on money one makes (e.g. an "income tax" or "un impôt sur le revenu") and "une taxe" refers to a tax on money one pays (e.g. a "VAT/TVA")?
Sure is. https://en.oxforddictionaries.com/definition/impost - It's even used in the US and Australian constitutions. It's not commonly used but I can assure you that the word is used in English.