Shoot, branch, bough, limb can mean one of the members of a plant and especially a shrub or a tree that are outgrowths from a main stem or from one of its divisions.
Shoot and branch are referable to most plants as well as to shrubs and trees and both imply development from a bud. Shoot, however, stresses actual growing and therefore applies chiefly to a young undeveloped member.
Branch suggests a spreading out by dividing and subdividing and applies typically to a more or less fully developed member, whether it arises directly from the trunk or stem or from an outgrowth or a subdivision of an outgrowth.
Bough is not interchangeable with shoot, for it usually suggests foliage and fruit or flowers. Although it is often used interchangeably with branch and is sometimes thought of as a large or main branch, it carries a comparatively weak implication of ramification and a strong connotation of full seasonal development; thus, bough may be preferred when the shrub or tree is in leaf or bloom and branch when the shrub or tree is stripped of foliage or its members are thought of as barren or dead.
Limb applies usually to a large branch that grows directly out of the trunk of a tree or to a member produced by the forking of the trunk.