In American English, period is the term for the punctuation mark used to end declarative sentences. In British English, the mark is usually called a full stop. Neither term is right or wrong. They’re just different ways of saying the same thing.
Full stop for the punctuation mark may be slightly older than period, but both date from the late 16th century. Period derives from the Latin periodus, meaning a complete sentence. Exactly how period went from this to referring to the dot at the end of a sentence is mysterious, but it’s not a great leap.
Full stop‘s exact origins are likewise not definitively established. It could be that the term came about to differentiate the mark from lesser stops such as colons and commas, or perhaps the term originated as a way to tell a transcriber that a sentence had ended. These are just guesses.
Outside the U.S. and Britain, full stop is generally preferred to period, but the latter does appear occasionally in all the main varieties of English. Full stop is comparatively rare in American English.
Both terms are sometimes spoken or written to indicate that a matter is settled—for example:
You are not getting a car for your birthday. Period.
We are not going to discuss it anymore, full stop!
They can also call attention to a statement’s having ended—for example:
Smoking is now regarded as not just bad for health, but bad, period.
This lead sentence is a mouthful. Put a period after “ago” and start a new sentence. [New York Times]
[T]he light punctuation, often using a line break in place of a full stop, pitches them somewhere between speech and writing. [Guardian]
Apparently, you paid more for punctuation than you did for four letter words, hence the use of STOP instead of a simple period. [National Post]
Mr Mitchell has opted for a comma in the middle of the slogan, whereas Ms Davis has inserted a full-stop. [Build.ie]