The "science" of biological classification is called "taxonomy".  All living things have been classified into a system accepted world-wide. The names for individuals are latinized and there is only one name for each species.  Latin is used because it is a "dead" language and will not change over time, unlike English or other modern languages.  For plants, the classification is largely based on flowers or reproductive organs of the plant.  There are various levels of groupings, beginning with general characteristics and becoming increasingly specific. These groupings are listed below.  Sometimes, intermediate classifications are used when a particular group of plants make it necessary.
     "Species" is the basic unit of taxonomy.   Sometimes, differences in appearance have been observed within a species and designations such as "variety" or "subspecies" or "forma" might be used.  A species, by definition, consists of "… a group of similar interbreeding individuals sharing a common morphology, physiology, and reproductive process … there is generally a sterility barrier between species, or at least reduced fertility in interspecific hybrids" [Society of American Foresters, 1998] .  Incidentally, the word "specie" is incorrect.  "Species" is the correct singular and plural form of the word.
     The use of "scientific" or "latin" names is important when looking at use and distribution of a species across geography or when interested in relationships among species.  All known living things have a two-part name which includes the genus and species names.  The genus name is always capitalized.  The species name is usually not capitalized.   "Populus tremuloides" can be recognized world-wide, but in Michigan it is known as popple, aspen, or quaking aspen.  Many trees have multiple common names that can be confusing when it becomes important to know exactly which tree you’re talking about.   And that's just in English . . . there are many other names in other languages.  It's easy to understand why we need a commonly accepted system of naming living things.

Kingdom: Plant (duh!)
Division: Spermatophyta (seed-bearing plants)

Class: Gymnospermae (all the softwoods/conifers)
  Order: Coniferales (all the softwoods/conifers)
    Family: Pinaceae (pines, spruces, firs, tamarack, hemlock)
    Family: Cupressaceae (cedar)
    Family: Taxaceae (yew)

Class: Angiospermae (all the hardwoods/broad-leaf trees)
(Note: from this point on, taxonomic classification varies among manuals)
Subclass: Dicotyledonae (2 "leaves" in the seed, not parallel-veined)
  Super Order: Amentiferae (has catkins)
    Order: Salicales
       Family: Salicaceae (willows, aspens)
    Order: Juglandales
       Family: Juglandaceae (butternut, walnut)
    Order: Fagales
       Family: Fagaceae (oaks, beech)
       Family: Betulaceae (birches, alder, hazel)
Super Order: Apetalae (flowers without petals)
    Order: Urticales
       Family: Ulmaceae (elms)
Super Order: Polypetalae (flowers with separated petals)
    Order: Rosiflorae
       Family: Fabaceae (locusts)
       Family: Rosaceae (cherries, Juneberries, apples, etc.)
       Family: Hamamelidaceae (witch-hazel)
    Order: Sapindales
       Family: Aceraceae (maples)
       Family: Hippocastanaceae (horse-chestnut)
    Order: Rhamnales
       Family: Rhamnaceae (buckthorns)
    Order: Malvales
       Family: Tiliaceae (basswood)
    Order: Myrtiflorae
       Family: Thymelaeaceae (leatherwood)
       Family: Elaeagnaceae
    Order: Umbelliflorae
       Family: Cornaceae (dogwood)
Super Order: Sympetalae (flowers with joined petals)
    Order: Contortae
       Family: Oleaceae (ashes)
    Order: Rubiales
       Family: Caprifoliaceae (viburnums, elderberry)