Images that are produced by a hardware (for example, the camera in your phone, or the camera connected to a telescope) provide pixelated data. Such data are therefore stored in a Raster graphics format which has discrete, independent, equally spaced data elements. For example, this is the format used FITS (see Fits), JPEG, TIFF, PNG and other image formats.
On the other hand, when something is generated by the computer (for example, a diagram, plot or even adding a cross over a camera image to highlight something there), there is no “observation” or connection with nature! Everything is abstract! For such things, it is much easier to draw a mathematical line (with infinite resolution). Therefore, no matter how much you zoom-in, it will never get pixelated. This is the realm of Vector graphics. If you open the Gnuastro manual in PDF format You can see such graphics in the Gnuastro manual, for example, in Circles and the complex plane or Distance on a 2D curved space. The most common vector graphics format is PDF for document sharing or SVG for web-based applications.
The pixels of a raster image can be shown as vector-based squares with different shades, so vector graphics can generally also support raster graphics. This is very useful when you want to add some graphics over an image to help your discussion (for example a \(+\) over your object of interest). However, vector graphics is not optimized for rasterized data (which are usually also noisy!), and can either not display nicely, or result in much larger file volume (in bytes). Therefore, if it is not necessary to add any marks over a FITS image, for example, it may be better to store it in a rasterized format.
The distinction between the vector and raster graphics is also the primary theme behind Gnuastro’s logo, see Logo of Gnuastro.