They are synonyms. "Office supplies" is much more common today in the United States. This is probably because it is the term used nowadays by the big stores that sell them.
"Stationery" has a range of meanings. The original meaning was limited to writing paper and envelopes.
When I was a kid, "stationery stores" were common, but they were fairly small in size. Even so, just as a "drugstore" sells many things besides drugs, a "stationery store" always sold many things besides stationery.
Staples changed everything when they introduced chains of huge stores selling a wide range of office supplies including desks and chairs, and now "office supplies" is more common.
By the way, you spelled "stationery" correctly, with an -ery. Note that it is a completely different word from "stationary" with an -ary, which means an adjective for something that doesn't move.