The meditation that we do in Seido Karate, and that's usually found connected with Japanese martial arts in general, is in the Zen style.
We say "Zen meditation", but technically that's redundant. "Zen" is the Japanese pronunciation of "Ch'an", which is the Chinese pronunciation of "dhyana", which is a Sanskrit word meaning "meditation". So "Zen meditation" literally means "meditation meditation"! But we usually mean it to mean a specific style of meditation: one that developed out of a certain school of Buddhism, but since the 13th century became more widely distributed throughout Japanese culture, and in the 20th century spread throughout the world.
So Zen is not the only type of meditation. For example there's Transcendental Meditation. That was big in the 60s, it was what the Beatles traveled to India to study, and seems to be enjoying a bit of a revival. Advocates claim that it will relax you or even bliss you out. (John Lennon talked about how the people he studied with acted like they were in a competition "to reach God quicker than anybody else", to see "who was going to get cosmic first." Lennon later realized, "What I didn’t know was I was already cosmic.") The Catholic tradition has its own type of meditation, really a form a prayer seeking contact with God -- definitely not what we do in zazen. "Mindfulness meditation" for stress reduction has become popular in recent years, and there are also guided meditations which are supposed to promote health or have various other benefits.