An artificially sweetened drink

I have to differentiate drinks with sugar and drinks with non-nutritive sweeteners.

It seems to me that a sweetened drink can refer to both, and that sweet drinks only contain sugar.

Is there any specific term for drinks with artificial sweeteners ?

Sentence example :

Drinks with non-nutritive sweeteners may be quite as bad for your health as sweet drinks.

NB : in French we have to word édulcorant, which means "which can give a sweet taste"

EDIT : the aim of my question is a scientific article. Thus I want to be as specific as I can.

We don't have a single-word term that I'm aware of. We might talk about "drinks with artificial sweeteners" for example. Or a drink might have an advert/label that says "no artificial sweeteners!".

You're correct that "sweetened" may be with sugar or may be artificial. We do have another adjective "sugary" which according to dicitonary.com means "sweet" or "excessively sweet", but I would only use it for things which contain actual sugar.

As to your sentence example, I'd probably use:

Drinks with artificial sweeteners may be just as bad for your health as sugary drinks.

In English such beverages are called diet drinks or sugar-free. As common as these names may be, their origins lie in advertising and the manufacturers who pay for it.

Until the recent emergence of a natural product, stevia, as a sweetener, artificially sweetened was accurate, since sweeteners such as aspartame, saccharine, or cyclamates are manufactured chemicals.

In the 1970's the number of beverages sweetened with high fructose corn syrup skyrocketed. In the advertising sense, then, a sugar-free beverage is one free of sucrose, fructose, or glucose.

I am unaware of a categorical term exclusive to these three sugars that would readily eliminate others such as maltose and lactose. So if sugar-free is not precise enough, your only option is first to use a longer expression, abbreviate it at its first mention, then use the abbreviation thereafter.

a beverage sweetened without sucrose, fructose, or glucose (non-SFG beverage)

This type of ad hoc abbreviation is common in academic writing, and if the abbreviation proves useful, others will begin to use it as well.

'So, is there any specific term for drinks with artificial sweeteners?' At present time: NO.

'It seems to me that a sweetened drink can refer to both, and that sweet drinks only contain sugar.' But that is not necessarily the case either. Some naturally sweet fruit drinks are further sweetened by either natural sugars, artificial sweeteners or both.

Lot of FDA food politics in the states re: food labeling of natural sugars, artificial sugars, and combinations! For those that need to absolutely know, check the labels and/or contact the manufacturer. Here is a nifty table with labeling guide: FDA artificial sweeteners

And then there is this:

Nutrasweet in Milk–With No Label? Find Out What’s Really Going On nutrasweet in milk without labeling This is a proposal by our government to allow a sweetener without labeling for the public good!

The word "sweetened" implies that an action has been taken to sweeten the drink. "Sweet" on the other hand, implies that the drink contains sugar. However, it has been widely, and incorrectly, used oftentimes, to refer to sweetened drinks.