Both of them mean to use bad words, but I don't know their differences. Please explain with some examples! Thanks!
The distinctions between curse and swear are not always recognized, because they have a clear usage overlap in the definition of foul language:
2.0 [NO OBJECT] Utter offensive words in anger or annoyance:
he cursed loudly as he burned his hand
2.1 [WITH OBJECT] Address with offensive words:
I cursed myself for my carelessness
2 [NO OBJECT] Use offensive language, especially as an expression of anger:
Peter swore under his breath
Curse is used as foul language with or without a direct object, while the foul language meaning of swear does not normally receive an object, except in the expression swear at:
John cursed the day he was born.
Jeff swore at the umpire, before he went back to the dugout.
Any minuscule difference between curse and swear at would be limited to the connotations of the definitions that curse and swear do not share in common:
1.0 [WITH OBJECT] Invoke or use a curse against:
it often seemed as if the family had been cursed
1.1 (be cursed with) Be afflicted with:
many owners have been cursed with a series of bankruptcies
1 [REPORTING VERB] Make a solemn statement or promise undertaking to do something or affirming that something is the case:
[WITH CLAUSE]: Maria made me swear I would never tell anyone
I swear by all I hold dear that I had nothing to do with it again,’ she swore, ‘will I be short of money’*
[WITH OBJECT]: they were reluctant to swear allegiance
1.1 [WITH OBJECT] Take (an oath):
he forced them to swear an oath of loyalty to him
1.2 [WITH OBJECT] Take a solemn oath as to the truth of (a statement):
I asked him if he would swear a statement to this effect
1.3 [WITH OBJECT] Make (someone) promise to observe a certain course of action:
I’ve been sworn to secrecy
Curse expanded to "foul language" in the thirteenth century from pronouncing evil on others:
Old English cursian, from the source of curse (n.). Meaning "to swear profanely" is from early 13c.
late Old English curs "a prayer that evil or harm befall one," of uncertain origin, perhaps from Old French curuz "anger," or Latin cursus "course." Connection with cross is unlikely. No similar word exists in Germanic, Romance, or Celtic. Curses as a histrionic exclamation is from 1885.
Swear expanded to "foul language" in the fifteenth century by way of profaning a solemn oath:
Old English swerian "take an oath" (class VI strong verb; past tense swor, past participle sworen), from Proto-Germanic *swarjan-, (cognates: Old Saxon swerian, Old Frisian swera, Old Norse sverja, Danish sverge, Middle Dutch swaren, Old High German swerien, German schwören, Gothic swaren "to swear"), from PIE root *swer- (1) "to speak, talk, say" (cognates: Old Church Slavonic svara "quarrel," Oscan sverrunei "to the speaker").
Also related to the second element in answer. The secondary sense of "use bad language" (early 15c.) developed from the notion of "invoke sacred names."
Although they are used interchangeably, for the most part, in the US we understand the difference when the speaker is obviously an immigrant - or, a member of a culture that passes it's superstitions on to each generation.
Perhaps because I am only a second-generation American, (and grew up around many relative newcomers) I know a "curse" when I see one.
In New York (melting-pot-central) we say: "I cursed him out," and "I swear to God," in a casual sense of venting frustration verbally.
"I cursed him," means that the supernatural was invoked
"I swear on my mother" is a blood-oath.
To avoid any misunderstanding, when the assault is merely a tongue-lashing, we say:
"I told him to go #$@! himself." (Or, "He told me to go #$@! myself.")
(The actual words used in the exchange do not alter this expression.)
To my mind, the practices are similar, but "cursing" is more creative. For example, the Seven Bad Words can be called "curses" or "swears". When I picture someone swearing at their car, I envision someone muttering the typical cusses under their breath:
"Goddamn stupid piece of shit." kick
when I picture someone cursing at their car, maybe they're using the usual bad words, but maybe they're injecting some new flavors:
"Idiot car not worth the trouble gotdamshIT!" kick
When I picture someone swearing at God, I picture someone who is frustrated but still using pre-defined acceptable words. When I picture someone cursing God, I see the same thing, but they're shaking their fist, too, and tearing up with rage.
Cursing seems a little more dramatic. Maybe because it carries over the "curse" connotation.
A curse can have another meaning than swearing, i.e. merely using bad language:
“I hope you die painfully” is a curse, wishing harm to another person. So a curse does not need a swear word, to express how you wish someone to die. Also, I believe it clearly expresses the intent of the heart.