In standard English usage, the word butt has numerous meanings as both a noun and a verb.
The OED offers 14 entries for butt as a noun. The meanings vary from “barrel” to “a type of one-horse cart.”
Perhaps the most common definition is
a. The thicker end of anything, esp. of a tool or weapon, the part by which it is held or on which it rests; e.g. the lower end of a spear-shaft, whip-handle, fishing-rod, the broad end of the stock of a gun or pistol.
Butt meaning “barrel” gives us the expression to be the butt of a joke. This use stems from the custom of setting up archery targets on barrels. The butt of a joke is the target of a joke.
The meaning “remainder of a smoked cigarette” was first recorded in 1847. The sense of “human posterior” has been in use from 1450, but ancient use does not necessarily confer acceptability in standard speech.
To my ears, butt as a word for the human posterior is for informal use, more or less on a par with bitch as used by some speakers as a generic term for “woman.” That’s why I was startled to hear it used in a television commercial the other night:
Better legs and better butt with every step.
To my ears the ads that use this phrase are more offensive than the ones with the baby bear who can’t wipe his bottom without leaving behind scraps of toilet paper. At least those ads use the word “bottom” for the anatomical area under discussion.
In mulling over my reaction to this use of “butt” in an ad intended to be aired in every living room in America, I reviewed the many expressions in English that can be used to refer to a person’s backside.
I’ve probably used them all at one time or another, but not indiscriminately.
Some words for the human posterior seem to me to be acceptable in ordinary speech, no matter who is present. For example,
Some I’d use only if I felt some irritation with the person whose anatomy was being referred to. For example,
fanny (Caution: this one does NOT refer to the same bit of anatomy in British English as it does in American English.)
ass (arse in British usage)
Some words I’d reserve for moments of jocularity or perversity:
As a copywriter I might use “butt” in an ad to be placed in a specialized publication read by young people, but not for one intended to be run during national television prime time.
It’s a generational thing, I’m sure. I hear plenty of young people use it as if it were perfectly acceptable in polite company. Still, advertisers might think twice about using it in ads intended for a general audience.