There are several kinds of classes in this scheme. The naming can often be ambiguous. That is why in taxonomy one has adopted the name “clade” for any group that belongs together. A clade then can be a Kingdom, Phylum, Class, Order, Suborder, Family, Subfamily, Tribe or Genus. The science of grouping or taxonomy has thus been named cladistics. One reason for using the word clade is that there are no good objective reasons why a clade should be a Family, Superfamily, Subfamily or Order. It is difficult to ascertain the level of a clade.
Phylogenetics is the study of evolutionary relatedness among groups of organisms. This is done these days through molecular sequencing data and morphological data matrices. The term phylogenetics derives from the Greek terms phyle, phylon, denoting “tribe” and “race”.
A very important trait of groups is that they should be monophyletic. A group, clade or taxon, is monophyletic means that it contains all the descendants of the, possibly hypothetical, common ancestor of the members of the group and no other organisms. A basic principle of phylogenetics is that clades should be monophyletic. Monophyletic groups are often characterised by shared characteristics, called synapomorphies. This is sometimes not the case anymore since the DNA analyses were introduced. For instance, the order Malpighiales has no synapomorphies. In phylogenetics one always tries to define monophyletic groups, clades.
A clade is said to be paraphyletic if the group consists of most but not all the descendants of a common ancestor. The clade is not complete, so to say. For instance the clade Gymnospermae is paraphyletic as the Angiospermae have the same common ancestor but do not belong to the clade Gymnospermae.
A group is called polyphyletic if the common ancestor is not a member of the group. An example is the group of carnivorous plants. They belong to several clades, families. One can say that polyphyly is an extreme example of paraphyly.
Some clades that are paraphyletic still form a well defined clade. Gymnospermae for example are paraphyletic but still seems to be a natural clade and are used as such. Gymnospermae have very typical common qualities like their naked seeds. But as a clade they are paraphyletic because the Angiospermae have developed out of them. I use the term prephyletic for such groups as it seems more natural to treat them as a group, clade.
The apparent contradiction arises from how evolution works. Evolution can be seen as a tree with branches. Each branch, with all its side branches and leaves, is a monophyletic group. But the main trunk is different, it develops always from a former group. That clade was monophyletic first but due to the new evolution becomes paraphyletic. Gymnospermae are strictly speaking paraphyletic because a complete new development arises out of them, the Angiospermae. Strictly speaking they should be treated as belonging to the Gymnopserms to make that clade monophyletic but that would make the clade awkward because the new aspects, the completely new qualities of the Angiospermae do not fit into the Gymnospermae.
For such situations I use the term prephyletic for clades like Gymnospermae Protidae, Fabanae, Malvanae.