Why don't we say alternating voltage and direct voltage instead of AC and DC?
I don't know for sure and I'm not sure if there's a book that discusses the etymology, or not. But I can take a shot at it which may help find an answer.
First off, we're discussing English and, as it turns out, Benjamin Franklin was the first person to construct a workable mental model to explain Leyden jars, the earlier German friction generators, and the concept of conduction. He was also pretty famous for other reasons and had the ears of the general public. He created the concept of an electric fluid to do that.
Volta developed/refined the battery pile, which at the time wasn't known for its voltage but instead for its current. It didn't produce sparks, but was used for its steady current in laboratories of the time. In fact, within weeks of his announcement of his piles, two English scientists (William Nicholson and Anthony Carlisle) were already using its currents in order to separate oxygen and hydrogen from water! Davy also immediately stopped his earlier efforts (he was 21 years old then) and shifted over to try and find out "what these amazing currents can do." [See note at bottom.]
It also got into "medical" use (muscle twitching, for example), which I think is again where popular use of terms occurs.
(Who, outside of engineering for example, immediately knows the origin of "push the envelope?" But yet the term is still widely used by the population, at large, too.)
Ørsted, not long after, found that magnetic effects could cause a current in wires and Faraday the very next year was able to show how to apply these two ideas to create a motor.
I suspect, but not having directly lived through that time myself I remain unsure of course, that Benjamin Franklin's fluid ideas were easiest for the lay public to put in mind when thinking about the developments taking place around them. And I suspect that the idea stuck. Marketing folks would have later simply leveraged the public's concepts when the "war of currents" began, and the ideas become set in verbal concrete.
A note about Davy: In checking on my facts above, I uncovered that Davy was an amazing popularizer of science and thought I'd share a few interesting bits I uncovered today. After starting to explore with Volta's battery piles, he soon transferred to The Royal Institution of Great Britain (in 1801, at the age of 22!!) One of the stated missions of the institution was to provide public demonstrations of science meant to stimulate an interest in science by the elite of the day (for monetary support, I suppose.) To achieve that, they created a theater in their building on Albemarle Street in London. Davy started out as an assistant lecturer, but the lectures at that moment were also dwindling in popularity and weren't serving the institution's hoped support from the elite. Davy was very soon "promoted" to this top job of public lecturing. To make the most of it, he chose to make his lectures seem "spontaneous" and "shocking." It worked! And almost the moment that Davy took over the lectures, the audiences were packed in. They quickly became so popular, in fact, that Albemarle street became the first one-way street in London because of all the carriages that were bringing people to hear his lectures. (Within 5 years or so, he was able to tell the Institution that he had filled their coffers well enough doing "their work" that he now wanted their support for him to go off and do his research.)
I found it very interesting to learn that the popularity of science demonstrations led to the first one-way street in London!!