Infinity referred to something being never-ending in space, whereas eternity referred to never-ending time.
In 1999, upon the resolution of the Great Kingdom reality, Anne Travers banished the Great Intelligence, where it rode the blue shift outwards into infinity. (PROSE: Millennial Rites)
Interstitial time had the appearance of infinity. (PROSE: Falls the Shadow)
Rondel, known anciently as the Arc of Infinity, was an inter-galactic region of space devoid of all stellar activity. (TV: Arc of Infinity)
According to the Tenth Doctor, the Chinese Ming dynasty had the "best dim sum this side of infinity." (TV: Dreamland)