Stationery means stationery goods, i.e. items sold by a stationer, such as paper, pens, ink, envelopes, and other office supplies and writing and printing material.
Stationary means immobile or apparently immobile, not moving, fixed in a station, or not changing in quantity, course, or condition.
Stationary also used to mean stationery; both terms derive from the Latin stationarius, stationery arriving indirectly by stationer + -y. The words have had distinct meanings for hundreds of years, yet they are still confused even by stationery companies (click image to enlarge):
At least the company’s website has the correct spelling.
EDIT: Here’s the same slip on the BBC News website:
If you have trouble remembering which is which, a mnemonic can help. You could picture a stationary car or van and think of the ‘a’ common to those words, or think of the ‘e’s common to stationery and letter or envelope. More elaborately, you could imagine a taxi driver called Harry who waits for you at the station. This is Station ‘Arry, and he’s not moving, he’s waving.