(In the following mathematical uses of terms are given in "quotes".)

So many of the names of mathematical objects are arbitrary and I think that can be harmful. "Real" numbers are just as imaginary as "imaginary" ones! They both have use in physics as models for natural phenomena, but neither are real like an atom. You may still argue that "natural" numbers are real because we really can have n of something, but general real numbers can't be written down or computer or used to divide physical space and time as we understand them now. The names are mostly historical artefacts that serve as mnemonics, nothing more.