My understanding is that herb is a pretty general term that includes all herbaceous plants, i.e. forbs = a herbaceous flowering plant that is not a graminoid; Graminoids = which encompass grasses (i.e. poaceae), sedges (cyperaceae) and rushes (juncaceae).
I'm not sure whether the term 'non-woody plant' can be used as a synonim of herbaceous plant, or whether it is a bit more general encompassing both herbaceous plants as well as other non-woody plants you would hardly call a herb (e.g. some cactaceae).
Very clear answer, Francesco. I might expand 'forb' to not just (herbaceous) flowering plants, but vascular plants. That would include ferns and fern allies.
Shall I add to Francesco and Truman definition about the Forb.
Forbs are herbaceous (not woody), broadleaf plants that are not grass-like. Grass-like plants include sedges (Cyperaceae) and rushes (Juncaceae). Forbs are herbs other than grasses. Examples include: comfrey, small burnet, and chicory. Sunflowers are becoming more popular as a forage forb.
Herbs should be gramineous plants (grasses, sedges and rushes) plus forbs; grass should be included in gramineous plants; grass-like plants should be gramineous plants except of grasses; non-woody plants should be broader than herbs, but refer to herbs fort most of the time.
Herb is a general term that includes forb (non woody plants with broader leaves and distinct flowers), ferns and fern allies, grasses, sedge and rush (grasses, sedge and rushes are non woody plants with long narrow leaves).
I consider herbs to be non-woody plants that die back to the ground after flowering. Grasses, sedges and rushes don't always do this, so I would put them in a separate category. I've always thought of forbs as "forage herbs", in other words, they are in a grassland context with grazing animals but they are not grasses (or grass-like) plants.
Grasses are usually herbaceous, which indicates that they produce a seed, do not develop woody tissue, and die down at the end of a growing season. Forbs are herbaceous (not woody), broadleaf plants that are not grass-like. Forbs are herbs other than grasses. Herbis any green, leafy plant, or parts thereof, used to flavour or season food. Non-woody plants (also called herbaceous plants) are plants that have no persistent woody stem above ground. They are classified following life-cycle classification as annuals, biennials or perennials.