Arms race + Cuban missile crisis

May 2015
I am slightly confused on the difference of the arms race and nuclear missile gap that occurred during the cold war. It would be great if someone could help me understand the difference or if they're the same.
Secondly, did Krushchev already have nuclear missiles in Cuba? and he was just sending more over but they were intercepted by the Americans or were the nuclear missiles that he was sending over in ships the first ones that were going to be placed in Cuba?
Thanks for your help in advance