You can sometimes find a bewildering range of terms when dealing with plants. All of them refer to the subject called taxonomy, the classification of living systems. I intend to explain the terms.
Firstly, plants belong to the kingdom Plantae, which includes all flowering plants. But the seaweeds belong to a different kingdom, and fungi belong to a kingdom between animal and plant. The difference between plants and fungi is very significant. Plants have roots and respire carbon dioxide in and oxygen out, whereas fungi have no roots and are air breathers. What people think are the roots of fungi are the hyphae, a network of threads that cluster together in a huge colony and which collectively produce a fungs as their spore-bearing body.
The basic unit of any living creature is a species, which is a kind of being that can reproduce with other members of the species and shares broadly the same characteristics. But you will note that there are terms other than species. All plants have a double barrelled name derived form Latin or Greek, for example Origanum majorana. The second word denotes the species and is always started with a lower case letter; the first word denotes the genus [plural genera] and has always a capital. The genus is the group of species to which a species belongs. Sometimes members of the same genus can breed together to produce hybrids. Occasionally you get hybridisation between members of different genera. Take an example. Leylandii are technically known as X Cypressociparis leylandii, as it is now known to be an intergeneric hybrid. Dianthus x allwoodii is an interspecies hybrid within the same genus.
Another term is variety. Take an example. Petroslinium crispum var tuberosum belongs to the species parsley, but has specific qualities, in this case a tuberous root that can be eaten. It can easily breed with other vareties of P.crispum, and the result will be a cross between them. Sometimes species have subspecies. S subspecies is a variety that seems restricted to a certain geographical area, or at least to thrive best in that limited location. The cricket bat willow is such a subspecies, as it flourishes best only in certain areas of the east midlands of England. You will ssp before the subspecies' name. You sometimes see a plant named, for example, Linicera periclymenum 'serotina' The word in quotaton marks denotes a cultivar. This is a variety artiifically created by humans and maintained only by breeding. Sometimes cultivars come in groups, for example Hydrangea aspera 'Villosa Group' This denotation is used to advise that all cultivars in a particular group are treated in the same way and planted in the same time window.
Below varieties are the form and the subform. These are varieties within varieties, and are generally only of use to flower growers. Vegetabe growers rarely, if ever need such a specific description.
A special term applies to orchids. Besides the genus and species, orchids have a grex. This is an extra name to denote the origin of an orchid hybrid. This is because orchid hybridsation has produced such a dazzling array of plants that an extra term was needed.
Above genus is family. For example Solanacea are the family to which potatoes, tomatoes, and the nighshades belong. Some families, such as the Rosacea, have many general and thousands of species cntained therein. Breeding between different familes is impossible. Families are grouped into orders and orders into classes, but these need not bother the gardener very much. There is a dazzling array of distonctions sucha s sub-order, super order and so on. But these are mainly for use by biologists