A basic plant name consist of a genus which starts with a capital letter and a species which does not both of which should be written in italic or underlined. This is to make it clear you are looking at a proper plant name. Good as this simple system is, and if that was it live would be a lot easier, often this is not enough and other bits get added. The most common for gardeners is a cultivar name (abbreviated to cv.) and this particularly good form of a plant which has been selected e.g. Photinia ‘Red Robin’ is a particularly good form of Photinia x fraseri and the cultivar name is written in normal type but enclosed in single quote marks.
So what is a genus? This is where things get messy. There is no nice neat definition of what actually constitutes a genus or a species. There are to lengthy codes lying down what is or is not a valid name, the International Code of Botanical Nomenclature and the International Code of Nomenclature for Cultivated Plants, both at which carefully avoid any definition of what constitutes a genus or species. In practice its all down to what people can agree on is a genus or a species. Guess what botanists often don’t agree and this leads to plant names being changed as people argue is this a genus or a species in a genus and so on. This is turn leads to the frequent complain that ‘they keep changing the *@*!* name’. The real problem plant names assume that all plants are related by evolution and the names should demonstrate this. So a group of genera will be placed in a family all of which have a common ancestor they evolved from. But this common ancestor is now extinct and lost to us. It’s rather like trying to work out if your neighbour is related to you with out any historical documents to refer to relying on appearance alone!
What you need of course is some sort of definition to tie down a genus and in practical terms a genus is a group of closely related species. This can on occasions be a group of one, but then is generally believed that there were other members but they have died out and become extinct. Similarly what a species is not that well defined. Traditionally a species was said to a group of plants which could breed with one another but then two different species could not be successfully crossed. This has a problem as gardens, and to a lesser extent the wild, are littered with plants which are the result of two species being crosses. Not to mention the number of plants which are the result of different genera being crossed! Really a species is a group of very similar plants, more similar that those included in the same genus, which look the same but are not genetically identical.
How many a dispute could have been deflated into a single paragraph if the disputants had dared to define their terms.
Greek critic, philosopher, physicist, & zoologist (384 BC – 322 BC)