The reason delta printers are named such is due to the 3 arms control the print head. Delta printers typically are shaped more like a tower, compared to cartesian printers, which are shaped more like boxes. Delta printers are known for their unique looks, but suffer from a slightly lower resolution in the center of the build platform, however they tend to be faster and are made of less parts. Delta printers are calibrated by their bed and by trigonometry - incorrect calibration will cause the print head to move in a wavy pattern over the bed.
The dominant type in its field, cartesian printers are known by their boxy or rectangular appearance. They operate by moving the extruder with a series of pulleys and belts, which are orientated horizontally. Cartesian printers are calibrated by bed and use geometric coordinates - thus are easier to deploy initially.