Let's make it clear: there are three levels of lenses. There are entry-level lenses. There are prosumer lenses. And there are the professional-grade lenses.
The "kit" lenses are the low-price, lightly built lenses, like the 18-55 and 55-200 lenses which are sold at VERY low prices--$200 or less. When people speak about kit zoom lenses, they are referring to the inexpensive, lightly built, low-cost zoom lenses. Every single kit zoom lens has a variable maximum aperture--every,single one.
The 24-105 Canon L series lens with Image Stabilizer was often sold in the $3,800 EOS 5D "kit"; however, a Canon Luxury-series, L-lens that sells for more than the price of most entry level d-slr kits, is clearly not a "kit zoom".
"Kit zooms" have been around for quite a while now. I think most of us know one when we see one. it is light, slow in aperture, and priced very affordably--well below the cost of a prosumer or professional-level lens. One aspect of kit zooms: for the most part, they are made by the camera makers,and not by the third party lens makers,although some might consider the low-priced,light-duty 70-300 models made by Sigma,et al to be kit lenses. For example, the 18-55mm f/3.5~5.6 kit zooms sold by Nikon,Canon,Pentax, and Sony--we do not see Tamron or Sigma or Tokina trying to get into that low-low end market; instead, Tamron and Sigma and Tokina are aiming for the prosumer level lenses with f/2.8 constant aperture, and a range beginning at 17,18,and 16mm respectively, and topping out at 50mm--those are not "kit zooms". Those are aimed at siphoning off the market for the Canon and Nikon 17-55mm f/2.8 "professional"-grade lenses made for APS-C cameras; the manufacturers' 17-55mm f/2.8 offerings cost more than the price of a body+kit lens, while the 3rd party prosumer lenses are in the $350-$400 range more or less.
Kit lenses are the "low-end" lenses, pure and simple. The absolute-cheapest are the 18-55 models, and the 55-200 models. There are also wider-range kit zooms, like Nikon's 18-105mm and 18-135. I think we can define kit lenses by what they are NOT; they are NOT expensive and they are NOT built to heavy-duty standards. The dividing line between kit lens and low-cost consumer zoom in the 70-300 category is marked by optical performance and price; most of the low-cost 70-300 lenses suffer from notable chromatic aberration at the longer end, while the manufacturers offer lenses that cost well over $500 that offer solid optics and are definitely prosumer zooms, approaching professional-grade in build and optics.
Let's put it this way: a kit lens is not a lens you'll be bragging about owning. Its origins are humble, its specifications quite limited, and nowhere NEAR state of the art.