Most of the images you see on web pages and Google images are raster images. They are pixelated images. If they are very low resolution they cannot work well for print and require editing. If they are high resolution they can be printed in many processes as is or require minor editing. Editing such as changing color and type is not possible, even the size may not be changeable.Raster file types: .jpg, .png, .bmp, .tiff
Vector images are graphic files that professional designers have created using points or vectors. They are the highest quality file and can be enlarged or reduced without affecting the quality. These files can also be edited very easily. Vectors can be exported as raster files but that eliminates its editing capabilities. These are great for company logos and clean line art designs.Vector file types: .ai, .eps, .cdr, sometimes .pdf
Spot color is what most screen printing and embroidery is based on. It's when each color in your design has a defined shape and a single color is used to fill the area. Very clean vector art is needed for this but it gives a crisp clean print.
Process color is what your desktop printer uses. Using CYAN MAGENTA YELLOW and BLACK to create any color. This would be used in photos multicolor images. Raster or vector images can be used but raster images must be high resolution.
Halftones used when trying to create shades of 1 color and making it appear to be more. These are what are used in printing process colors. The best example of this is newspaper prints. They are printed in black but use small dots to allow the do the shading. This is a great way to add to your design without cost.