STATIONARY: an adjective or adverb, meaning “not moving”, “fixed in one place”, “still.”
STATIONERY: a noun, meaning “paper, for letter writing or note-taking”

For example, “I use a stationary bike for exercise.” (adj)
For example, “The hostages were ordered to remain stationary.” (adv)
For example, “The girl received stationery and a special pen for her birthday gift.”

Stationary comes from the Latin “stationarius,” meaning “belonging to a military station,” while “stationery” comes from the Middle English noun “staciouner,” meaning bookseller.

TIP: “StationAry” means “still”, and when you are stationAry, you are often “stAnding.” “StationAry” also functions as an Adjective or Adverb (think of the As). In contrast, “StationEry” is papEr.