Mint is most usually considered a herb, in both senses of the word, although if you don't cut it back it can begin to turn woody.
Mint is a herbaceous plant that belongs to the mint family (Lamiaceae). It is typically a low-growing plant with a creeping habit and does not grow into a shrub, tree, or climber.
It is a fungus.
Lemon is neither an herb nor a shrub. It is a tree.
shrub
shrub
Shrubs
tree
A cucumber is a fruit (it contains seeds) but can also be classified as a vegetable.
Tree
Lemon plant is a tree, where the lemon fruits are growing. Those lemons, what we buy in grocery stores.
A bougainvillea is a shrub or small tree.
Technically it is called a herbaceous shrub