I'd caution against going into technical terms, which have their own unique (heh) definitions that aren't used the same as in daily life.

Yes, in math, there are normal random variables, exponential random variables, and uniform random variables. In daily life, when we say "random," we're usually thinking of a uniform random variable (rolling a dice). But in reality, when we say something is "random" in daily life, that something could be a dice, or it could be the weather, or height of waves, or whatever. Then, it could be a normal random variable, or a poisson, or whatever. So, it's actually correct for us just to say "random" in daily life because we haven't specified that we're talking about a uniform random variable. When I say something is "random" in daily life, I'm saying that it could be any kind of random variable, uniform or normal or whatever distribution it really is that I have no clue about.

But my caution is that it's quite possible that the word and definition for "random" came about before the mathematical definition for random and all its different types of randomness were developed. The daily definition of random doesn't need to listen to the mathematical definitions of random. We can separate these and let dictionaries separate their definitions as well, which they usually do. "Economics" comes from "household management, thrift," and thus we have the daily meaning of being "economic" as being frugal or expending little. Obviously, this meaning isn't used in the study of economics, where spending and investment and consumption is considered as important subjects of study as saving and not spending. So should economics change its name to something else, like "Moneyology" or "Resourceology," because they're misusing the word "economics"?

TL;DR Descriptivism, uhh, finds a way.