The hairstyle with short sides and longer hair on top is called an undercut.
In a classic undercut, the sides and back are buzzed very short or shaved, while the top remains noticeably longer. Unlike a fade, the length usually does not blend gradually from short to long; the contrast between the upper hair and the sides is the defining feature.
The style was fashionable from the 1910s through the 1940s, especially among working-class men and some youth gangs in Britain. Military haircuts during and after World War I also helped popularize short sides. The look later returned through new-wave and electronic-music subcultures in the late 1980s and early 1990s, then became mainstream again in the 2010s.
A pompadour describes hair swept upward and backward, not the side structure itself. A buzz cut keeps most of the hair uniformly short, while a fade gradually tapers the sides. An undercut can be combined with either a pompadour, slick-back, fringe, or longer textured top.