Back in January 2018, Variant Comics did a video breaking down why some speedsters have yellow, red, white, blue, and even black lightning.
Its starts off talking about former Flash and Titans artist Brett Boothe's reasoning behind the color selections. When asked directly on Twitter, Boothe's response was "the closer you go to light speed the colors shift. So red is the slowest. Blue and indigo are the fastest". When coloring speedsters he used the Blue Shift theory as a basis for his decision.
So future Barry in the Out of time comics series has blue lightning because he further tapped into the Speed Force and was much faster. In the normal comic continuity, the original Wally West was therefore faster than Barry Allan as Barry was yellow, and Wally was blue.
This changed during the course of the New 52 into Rebirth, at the start of New 52 barry had red lightning. By the events of Rebirth, he has yellow lightning, indicating that he has grown is power and speed. Because looking at the visible light spectrum and Blue Shift, it means that shorter wavelength is faster, and yellow is a shorter wavelength of light than red.
White lighting was used (according to Boothe) when speedsters were speeding up time. So white lightning was super fast, like Godspeed, who was so fast that he was able to be in two places at once.
So from the Comics perspective, there are your answers.