There’s a bunch, which is why it’s vague. Anything that can chemically set off our sweet tastebuds could, in theory, be considered a sweetener. Artificial sweeteners are generally those things that taste sweet and are safe to eat but can’t be used as fuel by our bodies, so they have little/no calories.
Aspartame is one of the oldest and best known (sold as NutraSweet and Equal, among other names). It’s purely chemical synthesis. Saccharine (Sweet’n’Low) is another like this.
Sucralose is another (trade name Splenda) that’s made from regular sucrose (normal sugar). So you can start from any plant that makes sucrose, like sugar cane or sugar beets, and then you chemically process it into sucralose.
There are many others. Mayo Clinic has a good list of the current FDA approved sugar substitutes: [Artificial sweeteners and other sugar substitutes – Mayo Clinic](https://www.mayoclinic.org/healthy-lifestyle/nutrition-and-healthy-eating/in-depth/artificial-sweeteners/art-20046936)
An artificial sweetener is just any substance that *tastes* sweet but contain few or no calories. There are a bunch of different ones. As you noted, some are derived from plants, and some are artificially created chemicals. Stevia is a common artificial sweetener that comes from a plant called *Stevia rebaudiana*. Another very common one is aspartame. Aspartame is a chemical that’s made in a lab. There are many more – too many to list. The Wikipedia page for sugar substitutes has a good breakdown of the various types of artificial sweeteners and a list of carious examples.
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