The scientific classification of Tree-of-Heaven and Old Man Cactus 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 Old Man Cactus kingdom and all other plants kingdom is Plantaea.
Plant family is the group of plants which have something in common. Tree-of-Heaven and Old Man Cactus family is a major factor of Tree-of-Heaven and Old Man Cactus 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 Old Man Cactus belongs to the family Cactaceae.
While comparing scientific classification, Tree-of-Heaven and Old Man Cactus genus and other classification are also important. Also, when you compare Tree-of-Heaven and Old Man Cactus, 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 Cephalocereus. Tree-of-Heaven tribe is Not Available and Old Man Cactus tribe is Pachycereeae. Tree-of-Heaven clade is Angiosperms, Eudicots and Rosids and order is Sapindales whereas Old Man Cactus clade is Angiosperms, Core eudicots and Eudicots and order is Caryophyllales. Every plant have subfamilies. Tree-of-Heaven subfamilies are, Not Available and Old Man Cactus subfamilies are Cactoideae. In this way you can compare scientific classification of Tree-of-Heaven and Old Man Cactus and other products also.