Way back when I was a Navy Cinematographer - that was when Noah (of the Ark fame) was one of my shipmates... We only called a lens a zoom lens if it retained focus at all focal lengths. An example of this type of lens was the 10-120mm Angenieux for 16mm cinema cameras. This was the standard lens that I used on the 16mm Arriflex when I wasn't using a three lens turret with a set of "T" Stop primes. The advantage to this lens was that I could zoom in to maximum focal length (around 120 mm) focus and then zoom out to my shooting focal length. Of course, this was in the days prior to any auto focus capability.
A lens that could zoom in focal length but, which did not hold its focus from one focal length to another was termed a variable focal length lens. The problem with this type of lens for motion picture or video shooting is that you cannot shoot while zooming from one focal length to another. However, since, I almost never zoomed while shooting, that would not have bothered me.
Today, with the advent of auto focus, the need to focus at the maximum focal length (to get a sharp image) is pretty well negated. I wonder how much my 100-400mm f/4.5-5.6 IS lens would cost and how heavy it would be if it could hold focus through the entire range of its focal length and if it had a consistent aperture throughout the focal range. How about adding internal focus to that equation... The cost and weight/size would be enormous
However, I am really happy with my 100-400 II lens because its sharpness and auto focus (especially when used with my 7D2) is marvelous. I love to be ble to count the individual hairs in a person's beard