Color Correction
Color Correction is a very broad term to represent the changing of color space in a piece of footage. While in the professional field corrections are usually exactly that - "corrections" to colors in a piece of footage, in the world of tennis usually the opposite is true. Manipulating colors introduces a huge world of intricate and abstract changes to existing footage.
Working with Color Models
Generally in the computer world, color is represented using the RGB Color Model (each color is made up of a mixture of red, green, and blue). These colors are then added together to create the final image. This is not the only color model (for example, the subtractive model CYMK (Cyan, Yellow, Magenta, Key) used in printers) but is most commonly used in terms of video footage.
When working in RGB mode, video editors will often have alternative space representations to make it easier to work with; one of the most common of these is HLS (or HSL). HSL space is a cylindrical representation of RGB that lets you make individual edits to the Hue, Lightness and Saturation of the image individually. Because of the cylindrical nature of the hue space, editors can "rotate" the hue around in circles to create a smooth rainbow effect. This is exactly how the infamous "rainbow effect" in Windows Movie Maker works (along with setting the footage monochrome).
Examples of these effects in common editors include "ProcAmp" in newer versions of Premiere and "Color Corrector (Secondary)" in Vegas.
Inverting Color
One of the most well known filters is the intentional "inverting" of colors. The effect is also known as "negative", like how a film camera photo negative will appear inverted until it is developed.
The most common (and most well known) inversion technique is through RGB space, however certain plugins (like the one in Premiere) can invert to other spaces, like HLS (re-mapping cylindrically) and YIQ.
A very common stutter loop variant is to invert every other frame.
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Inversion based on RGB color space. This is the most common type.
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Inversion based on HLS color space.
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Inversion based on YIQ color space. Notice the similarity to RGB inversion.
Tints/Recolor

A recolor or tint is to change a piece of footage towards a certain, particular color. in most editors, this is done by mapping the black and white values to different colors.
Tritone
A tritone lets you set color tints based on how close they are to white (the tint), gray (the tone), and black (the shade). This idea of recoloring is more in line with the actual definition of a "tint", rather than what is used by video editors.
Color Curves
Color Curves are a type of correction that allowed you to change color space based on a Bezier curve. This gives you an incredible amount of power as you can recolor things into whatever you want, from simple to extreme. Generally, color curve plugins let you change the red, green, blue and white values of RGB color space through a graph editor.

Color Curves are an effect in at least Vegas, Premiere Pro (removed in later versions, use the Curves function within Lumetri Color instead) and After Effects.