The scientific classification of Tree-of-Heaven and Red Cardinal 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 Red Cardinal kingdom and all other plants kingdom is Plantaea.
Plant family is the group of plants which have something in common. Tree-of-Heaven and Red Cardinal family is a major factor of Tree-of-Heaven and Red Cardinal 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 Red Cardinal belongs to the family Fabaceae.
While comparing scientific classification, Tree-of-Heaven and Red Cardinal genus and other classification are also important. Also, when you compare Tree-of-Heaven and Red Cardinal, 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 Erythrina. Tree-of-Heaven tribe is Not Available and Red Cardinal tribe is Phaseoleae. Tree-of-Heaven clade is Angiosperms, Eudicots and Rosids and order is Sapindales whereas Red Cardinal clade is Angiosperms, Eudicots and Rosids and order is Fabales. Every plant have subfamilies. Tree-of-Heaven subfamilies are, Not Available and Red Cardinal subfamilies are Faboideae. In this way you can compare scientific classification of Tree-of-Heaven and Red Cardinal and other products also.