No it's not, moving is just V E L O C I T Y
Accelerating is an I N C R E A S I N G velocity, and if it were accelerating it'd be mentioned in the question
Acceleration is a constant change in the velocity of an object, though while it IS moving, it is not the same as moving, because moving has no value or unit unless given. So to answer your question, yes they are similar but not the same.