Basically, yes. Stationery is stationer + y, meaning "goods sold by a stationer". Apparently a stationer was someone who sold books or writing materials. It originally meant someone who had a fixed station or shop rather than a travelling vendor. Stationary is from station + ary, meaning "having to do with a station" (i.e., being fixed or unmoving). But these both go back to the Latin statiōnārius. And stationery was frequently spelled stationary in the 1600s and 1700s. So both words come from the same root borrowed at different times in different forms.
For a good native English example, there's then and than and off and of. These pairs were originally the same words, and they differentiated in spelling and and meaning based on stress. In certain functions, the words tended to be unstressed, leading to reduced vowels and the voiced f in of. In other functions they retained their stressed forms (though than is frequently unstressed too, leading to homophony with then).
