/word nerd mode on
It's kind of interesting to consider how all of the so-called dirty words got their start. Historically, a swear or an oath is a promise before God that your words are true and you'll do what you say. If a person swore with an oath and then broke their promise, they were considered to be profane (treating something sacred with irreverence or disrespect) or to have uttered profanity. So in that sense, the words oath, swear, and profanity are all connected in that they all have to do with invoking the name of God or Jesus Christ.
Historically, the word "vulgar" merely refers to that which is common. For instance, Vulgar Latin was the everyday speech of the Roman people. Nothing dirty or low about that. Now however, the term "vulgar" has come to mean "coarse or crude." All of the dirty words that deal with "coarse or crude" aspects of our humanity (words for bodily functions, organs and acts, for instance) would be considered vulgarities.
So technically in this meme Kirk is requesting a swear, and Mr. Spock responds with a vulgarity, a mistake he most certainly would never make because that would be fucking illogical.
/word nerd mode off