The scientific classification of Tree-of-Heaven and Flame-of-the-forest includes the entire classification chart that includes kingdom, family, clade, tribe etc. A kingdom is the second highest taxonomic rank. A taxonomic rank is the level that a living organisms are placed in hierarchical level of arrangement of life forms. All the living organisms are divided into kingdoms. Plant kingdom is a main classification of living organisms that include all plants. There are six kingdoms which are: Plantae, Animalia, Fungi, Protista, Aschaea/Archaeabacteria and Bacteria Eubacteria. Tree-of-Heaven and Flame-of-the-forest kingdom and all other plants kingdom is Plantaea.
Plant family is the group of plants which have something in common. Tree-of-Heaven and Flame-of-the-forest family is a major factor of Tree-of-Heaven and Flame-of-the-forest Scientific Classification. Plant family helps you narrow the search of your plants. It also gives you idea about, how the plant looks, how the seed will be like etc. These two plant families can be different or same. Tree-of-Heaven belongs to the family Simaroubaceae and Flame-of-the-forest belongs to the family Fabaceae.
While comparing scientific classification, Tree-of-Heaven and Flame-of-the-forest genus and other classification are also important. Also, when you compare Tree-of-Heaven and Flame-of-the-forest, other factors should also be taken into considerations like order, subfamilies, tribe, clade etc. First plant's genus is Ailanthus and other plant's genus is Butea. Tree-of-Heaven tribe is Not Available and Flame-of-the-forest tribe is Phaseoleae. Tree-of-Heaven clade is Angiosperms, Eudicots and Rosids and order is Sapindales whereas Flame-of-the-forest clade is Angiosperms, Eudicots and Rosids and order is Fabales. Every plant have subfamilies. Tree-of-Heaven subfamilies are, Not Available and Flame-of-the-forest subfamilies are Faboideae. In this way you can compare scientific classification of Tree-of-Heaven and Flame-of-the-forest and other products also.