If you don't want details, here's the summary:

Left picture is printed with spot colors. (at least the green is a spot color)

Right picture is printed with 4-color process and shows the screened dots.

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4 color process printing is the method most commonly used. That means magazines, newspapers, and poker chip inlays. The dots are created with a screen and one would refer to the resolution as "line-screen". Newspaper might be 60 or 75 line-screen. A high qualiy magazine or coffee table book might be 150 line-screen or more. Higher numbers mean more (smaller) dots and finer detail.

When designing for print and you do not want the pattern of dots from from a screen, you specify a "spot color".

A spot color is a solid that has been pre-mixed to the specific color you want. This is done for various reasons (most commonly for consitency with brand colors: coke red, kodak yellow, fuji green, home depot orange, etc). On a poker chip you want it because the printing is so fine the dots become visible at a normal viewing distance. Also 4-color process printing does wierd things on textured inlays (the texture works like a lens, enlarging some dots and shrinking others).

Pantone is a company that makes ink and dominates the spot-color industry. Most spot colors are noted by their Pantone name. For instance my company's logo uses Pantone 426C.

4-color process and spot colors can be mixed. So you might have a 4-color print with 1 (or more) spot color added. Look at the top of many cerial boxes and you can see 4 spot colors (always cyan, magenta, yellow, and black) plus the spot colors (specific brand colors).