All vertebrates (including humans) have the same basic body plan: they are strictly bilaterally symmetrical in early embryonic stages and largely bilaterally symmetrical in adulthood. If they are divided down the middle, in other words, they have mirror-image left and right halves. For those reasons, the basic directional terms can be considered to be those used in vertebrates. By extension, the same terms are used for many other (invertebrate) organisms.
While the terms are standardized within specific fields of biology, there are unavoidable, sometimes dramatic, differences between some disciplines. For example, differences in terminology remain a problem that to some extent still separates the terminology of human anatomy from the one that is used in the study of various other zoological categories.