Comment by preseinger

a program which is concurrent expresses logically independent paths of execution, which can be executed one after the other, or at the same time, or any mix thereof -- it is a logical property of the program as expressed, and not necessarily exploited, or observable, when the program is run

a program which is parallel actively demonstrates multiple paths of execution during runtime -- it is a physical property of the program as executed

tl;dr: every parallel program is concurrent, not every concurrent program is parallel