In the US, the words "swearing" and "cursing" are used interchangeably meaning the same thing...using "naughty" language ("I swear" is a phrase that means, "I really mean it". To curse out someone means to use profane words towards them ("I cursed my cheating fiance out when I found another woman's underwear at his house).
An American comedian name George Carlin famously told a joke as part of his standup routine about the "7 words you can never say on TV". Although it's a few decades old, it pretty much still holds true in the US, with exception of like 2 words...you'll never hear them on non-cable/broadcast TV.
That being said, profanity (words and gestures both) is relative to where you are in the world. Something as innocent as holding up a single finger to indicate the number 1 to someone can mean a whole lot more in other parts of the world, even the finger you use matters.
Another example, in the US, cunt is a pretty offensive and abrasive word. In the UK and Australia it's not as strong of a word.