Definitely not. There are several aspects to this apart from the confusing ways in which the behaviour of  light differs from that of sound, but think of this: suppose you are drifting in a boat at a lower speed than the waves raised by your bow. The waves will move ahead of the boat and will increase their lead as they go.(There are some over-simplifications in my description, but in real life things are always too complex to deal with in detail! Try to concentrate on the bits that matter.)

Those water waves also will keep the same distance apart. We call that distance the wavelength.  The number of waves passing a point in a second also will remain the same. We call that the frequency.

Now, suppose you speed up, but still travel more slowly than the waves. They still will travel at the same speed, still will gain on you, but will not gain so fast, so each new wave you make will be closer to the previous one than the way it happened before.

The waves being closer together will mean that their wavelength will be shorter, and that more of them will pass any point at any given time. In other words, their frequency will be higher. But remember that their speed has not changed. Behind the boat the wave's frequency will change by the same amount in the other direction.

This is called the Doppler effect. Most famously it is something that we hear rather than see. Doppler first demonstrated and analysed the effect by experiments on a moving train with a trumpeter on board, but we all hear the effect any time a fast-moving source of sound passes close to us.  The sound behaves in all ways the same as ever it did, but its frequency rises as the source (for example the trumpeter on the train) approaches, and drops as it passes.

In the example of light waves much the same thing happens, but when the frequency/wavelength of light changes, the way we see it is in a change in COLOUR. When the light is from a source that is approaching us, such as the car's headlights, the waves' frequency and energy increase and their colour changes in such a way that they get closer to the blue end of the spectrum: we call that "blue shift" Coming from a source moving away from us, the light reaching us still travels at exactly the same speed, but its energy and frequency are lower, so the colour moves toward the red end of the rainbow spectrum. (And, yes, that is true for a car's tailights. We call that "red shift", even though it has nothing to do with the colour of taillights! )

At speeds that we usually see on Earth, the red or blue shift of light are important for many reasons, but we need very special instruments to measure them. They are far too slight to see by eye. The only place outside the laboratory where speeds are great enough to give a a really big red or blue shift is in very distant outer space, where we can tell whether stars or galaxies are moving towards us or away, by checking on their colour shift.

And even that requires special instruments!

Go well,

Jon