Build, construct, erect, frame, raise, rear are comparable when they mean to form or fashion a structure or something comparable to a structure.
Build strictly implies a fitting together of parts and materials to form something which may be large (as a house, a factory, a church, or a bridge) or small (as a bird’s nest, a fence, or a child’s toy) but of which the forming must involve some measure or degree of complication in the bringing together of parts and materials.
When used in reference to something immaterial build (often followed by up) may suggest an analogy between the immaterial thing and an edifice especially by implying an adding of part to part or bit to bit in the attainment of an end.
Construct comes close to build in its implication of the putting together the material given or at hand to form something. But it is not quite equivalent, for it stresses not the labor, especially the manual labor, involved but the problem involved in the fitting together of parts.
Construct therefore emphasizes the discovering by the mind of how the parts or the materials should be combined in order to gain the desired end.
To build is the work of men who use their hands or by analogy their brains to bring something into being; to construct is the work of men who use their brains, though sometimes their hands in obedience to their brains, to solve the problem of how a thing should be or is built or made or brought into being; hence construct implies composition or design and may take as its object anything brought into material or immaterial existence by one or the other process.
Construct is also often used as the opposite of destroy without a specific reference to these implications.
Erect basically means to set upright. Although the term may carry this as its essential meaning, it was early applied to high structures and has accordingly come to imply building in its most usual sense.
The word is often used in place of build without any marked implication of putting together parts and materials, but it always carries some suggestion of the sense of to set up (as by building or establishing).
Frame approaches construct but in respect to physical structures more specifically applies to the bringing together and joining of parts (as sills, plates, and joists) that define the form of the final structure.
In extended use it throws the stress upon a forming or fashioning to suit a design, an intention, a purpose, or the facts and may be applied to anything so constructed.
Raise and rear (see also LIFT) often replace build, especially when the idea of height is emphasized.