As another poster replied, horizontal defleciton is related to high voltage; you rarely have one without the other.
Vertical deflection has a lot of components driving it, and bad solder joints are a very common problem after a TV is several years old. But horizontal deflection failure, when it does happen, is usually caused by a bad connection on an inductor or a connector. There are just so many more opportunities for failure in vertical deflection.
Sometimes, when viewing a pile of TVs at the thrift shop, you'll see phosphor burn along the top of the screen. This is caused by failure of electrolytic capacitors in the vertical deflection circuit, causing a problem called "foldover." The electron beam is drawn more often in the topmost section of the tube than it should be, leaving a burn.