Well, I would agree with the meteorological definition, that's the one I was taught in my physics class as well. Wikipedia says:
In physics, velocity is the rate of change of displacement (position). It is a vector physical quantity; both magnitude and direction are required to define it. The scalar absolute value (magnitude) of velocity is speed [...]. For example, "5 meters per second" is a scalar and not a vector, whereas "5 meters per second east" is a vector.
Edit: so much for the difference between velocity and speed, since that is what you are expressly asking for. However, for the sake of completeness, I think I should add that "velocity" and "speed" sometimes are used interchangeably. For example, Merriam-Webster says:
Definition of VELOCITY
1 a : quickness of motion : speed <the velocity of sound>
b : rapidity of movement <[my horse's] strong suit is grace & personal comeliness, rather than velocity — Mark Twain>
c : speed imparted to something <the power pitcher relies on velocity — Tony Scherman>
2 : the rate of change of position along a straight line with respect to time : the derivative of position with respect to time
3 a : rate of occurrence or action : rapidity <the velocity of historical change — R. J. Lifton>
b : rate of turnover <the velocity of money>