Vertical integration is simply a more complex version of horizontal integration, first we need to understand the basics of what horizontal integration is.
It is a method of claiming the market and causing sales to grow, this is achieved by taking over a similar company, this strategy works for multiple businesses regardless of where they are situated, for example Coca Cola could take over a similar company in Africa etc.
Vertical integration however involves multiple steps that a company or entity may take to gain more power in the marketplace, this may not necessarily mean that the rival/victim company gets completely taken over it just involves some power to be moved around and market shares begin to grow in said company,mainly it includes having one lone distribution or producer working on the one product instead of spreading out the work and product.
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