Template:M comp disc Equity Derivatives 12.1(b)
Basically, they are all ways of combining businesses. The difference is identity of the resulting entity.
Merger
A merger is the combination of two or more companies into a single one, where one of the companies you started out with at the beginning is left at the end: this is the continuing entity. A takeover is really just a form of merger: the difference between them is really one of relative size. A bib bastard of a company takes over a smaller one; two similar sized companies merge. Either way, at the end, only one company remains. The other has dissolved itself into the stomach lining of its acquirer, its assets and liabilities slipping easily down the gizzard.
Consolidation
Consolidation, known in some places as amalgamation, is the action of combining two or more companies into a single new company. Unlike a merger, in a consolidation, none of the originally joining companies survives: in the consolidation process a brand new company is incorporated and all the assets and liabilities of all of the joining companies are transferred to the new entity. At some profound metaphysical level — a place that appeals at a deep, subconscious level, to legal eagles though they don’t understand it and cannot rationalise it, but it manifests itself in them having to describe it, bloody-mindedly — these things are profoundly different. But from a practical point of view — meaning we are excluding tax considerations, needless to say — they are exactly the same.
A share exchange is a way of combining businesses in which shares of one company are exchanged for shares of another. However, unlike in a merger, where only one company survives the interaction, or a consolidation, where neither comnpany does, in a share exchange both companies continue to exist as separate going concerns, though they are now part of the same consolidated group and will have some kind or other of a familial relationship (being a parent, child, siblings, long lost cousins from Australia, black sheep of family etc.)