You can say both, actually! In America, I would say "I'm tanning." This would include laying in the tanning bed in the salon. You cannot say you are sunbathing in the tanning salon, only I'm tanning would be appropriate then.

Hi Elisabetta, I don't agree that tanning and sunbathing are exactly the same thing. To sunbathe is to lie in the sun. Maybe to get a tan, or maybe to get warm. To tan would be to lie in the sun with the intention of getting a tan, or to go to a tanning salon, again with the intention of getting a darker complexion. The intention and location are different between the two terms. Therefore, if someone said to me "i'm tanning" I would assume they are going to lie on a tanning bed or apply tanning cream. If someone else said to me "i'm sunbathing" that would mean that they are lying in the sun, probably on the beach or in a park.

Both are correct. It would be more common to say "I'm tanning" though. In my opinion, when someone says "I'm sunbathing", it's kind of like they are trying to say "I'm tanning" in a high class way(they are trying to be fancy about saying it). So it's mainly said differently, depending on the type of person someone is. It would be more common for a high class(very wealthy or acting like they are very wealthy) person to say "I'm sunbathing". And it would be more common for the average speaking person to say "I'm tanning". But if you are getting a tan from a tanning bed, I'm not absolutely positive, but I don't believe it would be correct to say "I'm sunbathing", being as that you are not actually in the sun to get a tan....... And some people(mainly alot of guys) say the expression "I'm catching some rays" when we are laying out at the beach getting a tan. We say it like that so we don't sound feminine(girly). It is a more chill/relaxed/non feminine way of saying "I'm tanning", and means you're body is absorbing the heat "rays" from the sun. But women/girls say "I'm catching some rays" too, just not as often as men do. So unless you're tanning in a tanning bed, then "I'm tanning", "I'm sunbathing", and "I'm catching some rays" all mean the same thing, but "catching some rays" is more of an expression common for men to say. I hope that helps you bye :)