Carrie and Michael at a reading

A reading is just the actors performing the play by reading it. There are no props, scenery, costumes, etc. The actors just sit or stand in front of a microphone and read the script. They act with their voices. However, the actors are not doing a cold read. The play is rehearsed till all the nuances are perfected. A reading is also equivalent to the way plays were done for the radio.

Here's a picture of Michael at a reading:



A readthrough is when the actors see the script for the first time. They usually sit in a circle and read their parts. Sometimes, they are able to act the scene, sometimes not. It just gives them a feel of what the ensemble will sound like. It is also the last time that they will enact the play in the order it was written before the final rehearsals. Rehearsals are such that scene 1 may be rehearsed after scene 7, and so forth.

Does this clarifies it for you?