Thuja v Arborvtiae v Cedar

Thuja in common English is referred to as Arborvitae or Cedar, they are the same thing.

We are constantly creating new SPECIES, many thousands a year (as of 2023), often without assigning a name (identified only by a number) unless the SPECIES goes into commercial production in which case it will receive a name by the owner of the SPECIES.

A SPECIES developed by breeders goes into commercial production when they appear to have superior attributes to native and currently existing SPECIES. I.e. grows faster, more drought tolerant, more pest or deer resistant, more ornamental uniformity, etc.

Important details to consider:

Plant taxonomy is the science that finds, identifies, describes, classifies, and names plants. It is one of the main branches of taxonomy (the science that finds, describes, classifies, and names living things), (Taxa = Group, Nomy=Name).
Common name is a name we assign to plants, often a plant will have many differing names originating from different part of the vast English speaking World.

Classification (Grouping of plants):