A Reader is someone who in a particular liturgy is assigned to read a Biblical text other than the Gospel. (Reading the Gospel at Mass is reserved specifically to the deacon or, in his absence, the priest.) But it also has the more precise meaning of a person who has been “instituted” as a lector, and so is a lector even when not assigned to read in a specific liturgy.
The General Instruction of the Roman Missal speaks as follows of those who, without being lectors in the specific sense, carry out their functions at Mass:
“In the absence of an instituted lector, other laypersons may be commissioned to proclaim the readings from Sacred Scripture. They should be truly suited to perform this function and should receive careful preparation, so that the faithful by listening to the readings from the sacred texts may develop in their hearts a warm and living love for Sacred Scripture” GIRM 101.