Previously we discussed two words for ships - sefina and oniya. However, unlike that pair, where both words have biblical origin, and in modern Hebrew they define different size boats, the pair we'll look at now - matos מטוס and aviron אוירון - are both modern and refer to the same item: an airplane.
Why are there two different words? Pretty simple - they were coined by two different people. Aviron was coined by Eliezer Ben-Yehuda (some say his son Itamar Ben-Avi) in 1909, on the basis of the Talmudic word avir אויר - "air" (borrowed from the Greek aer.) Rosenthal suggests that the French word for airplane - avion - might have also influenced aviron.
Ben Yehuda also suggested the participle me'ofef מעופף, from the root עוף, "to fly", would refer to both the passengers (and pilot) as well as the action of the plane.
The poet Chaim Nachman Bialik preferred for mechanized flight the root טוס, also meaning "to fly", and from here came up with matos, as well as tayas טייס - "pilot", and tisa טיסה - "flight."
Today matos is almost exclusively used by Hebrew speakers for airplane, with the exception of young children, and some who use a more archaic Hebrew (such as those who haven't lived in the country for many years.) Nissan Netzer in Hebrew in Jeans (pg. 52) writes that matos might have overcome aviron due to it being a shorter word, with stronger consonants (a phenomenon he notes happens frequently when a foreign slang word becomes more popular than a native Hebrew one, like shok שוק (shock) instead of helem הלם or speed ספיד instead of mehirut מהירות.)