text message

noun
1.
an electronic message sent over a cellular network from one cell phone to another by typing words, often in shortened form, as “l8t” for “late,” on the phone's numeric or QWERTY keypad.
Compare instant message (def 1).
British Dictionary definitions for text message

text message

noun
1.
a written message sent by means of a mobile phone
Contemporary definitions for text message
noun

any short electronically transmitted written message, esp. those sent to a handheld device such as a pager, PDA, cell phone