A bitmap-based program stores the picture by giving the color of each pixel in the rectangular pixel matrix. A vector-based program does it differently. It stores curves and shapes by giving the coordinates of the corners and the corresponding color.
vector graphics need less storage than (unpacked) bitmap graphics. Also if you magnify bitmap graphics, you just get a coarse picture. If you magnify this small picture created by Corel Draw, you get this . On the other hand, magnifying a vector graphics creates new details.
Here is discussion of vector versus pixel for logo design.
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