wild pear tree, crabapple tree
棠 refers to specific fruit trees: the wild pear and the crabapple. The character centers on these particular tree species rather than a broad abstract concept.
棠 combines 木 (tree) with what is likely a phonetic component (the upper part, historically perhaps 尚 or a similar element). The character was used to name specific fruit trees, with 木 indicating the semantic category.
The bottom 木 is a tree. The top part looks like a little crown of leaves and fruit. Picture a tree with a distinctive crown bearing wild pears or crabapples.
For トウ, imagine a tall tree (棠) with a toe-shaped fruit: toe -> トウ. The wild pear tree has fruit that looks like a big toe hanging from the branches.