Do they mean the same "a men-only party" or are there differences in their specific usage?
Here is the entry for stag party in Harold Wentworth & Stuart Flexner, Dictionary of American Slang, first edition (1960):
stag party 1 A party attended by men only, often for the purpose of viewing obscene performances or movies, telling obscene jokes, and the like. 2 Specif., such a party given in honor of a prospective bridegroom by his friends.
Robert Chapman, New Dictionary of American Slang (1986) doesn't give stag party a separate entry, but mentions it in the entry for stag:
stag 1 n fr early 1900s A man who goes to a party alone, without a woman partner 2 adj For men only; without women: a stag function 3 adv: Several of the brothers were [going to the dance] 'stag'—P Marks [Plastic Age (1924)] 4 n (also stag party) A party for men only: His shoulders were as broad as broad as the jokes at a Legion stag—J Evans [Halo in the Blood (1946)]
Robert Chapman & Barbara Kipfer, Dictionary of American Slang, third edition (1995) alters the wording of definition 4 in Chapman from "A party for men only" to
A party for men only, as a bachelor party
As for the term bachelor party, in the United States it almost always refers to a "farewell to bachelorhood" party thrown for a soon-to-be-married man by his male friends. An example of this usage is evident in the subtitle to James Oliver Cury, The Playboy Guide to Bachelor Parties (2003):
Everything You Need to Know About Planning the Groom's Rite of Passage—from Simple to Sinful
A Google Books search for "a bachelor party" turns up a match from not later than 1826 in which the term seems to refer simply and generally to a gathering of single men, without any hint of wild behavior, sexual hanky-panky, or imminent matrimony. From William Beattie, Journal of a Residence in Germany, volume 2 (1831):
[Meiningen] 28th — I dropped in at a small bachelor's party this evening, and just in time to hear the conclusion of a warm debate on the respective merits of black and blue eyes. Both, it appears, are doing mischief,—but perhaps unconsciously.
Likewise Dickens's The Posthumous Papers of the Pickwick Club (1838) devotes a chapter to "A Bachelor's Party, Given by Mr. Bob Sawyer at His Lodgings in the Borough." This party involves a large supper, copious drinking, some choruses of "A Frog He Would a-Courting Go," and multiple intrusions by an irate landlady, who eventually sends all of the guests home.
It's not unthinkable that bachelor party may still occasionally be used to refer to any party to which only unwedded men are invited—in which case it would have approximately as general a meaning as stag party—but I haven't found an instance of such use in recent Google Books search results.
The emphasis on obscene activity in the 1960 Wentworth & Flexner entry for stag party, by the way, explains the emergence of the slang term stag film, which (in the Mad Men era and afterward) referred to pornographic movies often shown at all-male get-togethers.
According to wikipedia: Yes they are the same.
"A bachelor party (in the United States), also known as a stag party, stag night, stag do (in Great Britain, Ireland, and Canada), a "buck's party" (in Australia) or a maanhaar partytjie (in South Africa),[…]"