With the rise of phylogenetic nomenclature, the use of evolutionary grades as formal taxa has come under debate. Under a strict phylogenetic approach, only monophyletic taxa are recognized. This differs from the more traditional approach of evolutionary taxonomy. The difference in approach has led to a vigorous debate between proponents of the two approaches to taxonomy, particularly in well established fields like vertebrate palaeontology and botany. The difference between the statement "B is part of A" (phylogenetic approach) and "B has evolved from A" (evolutionary approach) is, however, one of semantics rather than of phylogeny. Both express the same phylogeny, but the former emphasizes the phylogenetic continuum while the latter emphasizes a distinct shift in anatomy or ecology in B relative to A.As it says, the use of paraphyletic groups doesn't really change the meaning of anything, but rather the emphasis. It's kinda out of fashion amongst professional paleontologists, but in going that route, they've made things extremely inconvenient, not only for themselves but especially for non-specialists. Phylogenetic nomenclature, and the insistence on only monophyletic groups lacks a certain common sense.
Let me give an example. Dinosaurs. One of my first loves. Dinosaurs, as commonly understood and referred to by both specialists and non-specialists alike is actually a paraphyletic group. Because birds are descended from dinosaurs, according to phylogenetic nomenclature, birds are dinosaurs. Therefore any discussion of dinosaurs includes birds, and references to the extinction of dinosaurs are somewhat nonsensical, since there are somewhere around 10,000 species of birds today; more than any other type of tetrapod. Dinosaurs are kinda the big elephant in the room that proponents of phylogenetic nomenclature seem to ignore. I've never really heard anyone say the word dinosaur in the monophyletic sense. Everyone uses the word in a paraphyletic sense, i.e., dinosaurs excluding birds. The only exception is when the discussion is specifically about bird-like dinosaurs or the specific transition from dinosaurs into birds. When in that very narrow gray area, the distinct shift in anatomy/ecology is maybe not quite as distinct, but again--that gray area is very narrow, and otherwise, emphasizing the change from dinosaurs into birds--an evolutionary approach--is not unusual.
There's a few other paraphyletic groups that paleontology enthusiasts are likely to use because they're simply too convenient, and it's really unwieldy to use the correct terms according to the rules of phylogenetic nomenclature. Pelycosaurs, for example. Or their descendents, therapsids. There's a lot of reasons to talk about pelycosaurs exclusive of therapsids, or therapsids exclusive of mammals. Amongst dinosaurs, prosauropods, hypsilophodonts and igunodonts, exclusive of their descendents, are also incredibly convenient and I see them used all the time (frequently with an unwieldy caveat that the user "shouldn't" be using it.) Thecodonts is another one. Non-dinosaurian and non-crocodylian basal archosaurimorphs, archosauroforms and archosaurs is just ridiculous.
I feel a bit justified in learning, however, that a few years ago over 150 biologists of various stripes wrote a joint letter to the academic publication Taxon in defense of the idea of paraphyletic taxa. I don't know how significant that is compared to the numbers of working, academic biologists, but keep in mind that less than 5% of working astronomers voted on the definition of a planet question--a definition that is certainly not without controversy. For the better part of 15 years--or maybe even longer--I've seen phylogenetic nomenclature presented as if it were a done deal in the academic, scientific community, and that the use of paraphyletic taxa was only the result of legacy or imprecision used informally. Although, frankly, even if that were the case, those aren't necessarily bad things.