The term 'organic' denotes the way living beings develop from the womb. Time plays a crucial role. Inorganic growth is like assembling built parts (organs) into a system. For many businesses, the way forward is growing organically for the first say two to three years. For an online business, you come out with a proprietary software, unique contents, find affiliates and sponsors, build followers and customer list, raise MozRank. This comes close to organic Search Engine Optimization (SEO) where the focus is on generating unique contents and notion of time comes into play.
Organic growth gives an impression of sticking to one place, slow movement, guarding home/core territory. The idea is finding meaning with roots. For months, your business may be generating little revenue. Your confidence in what you are doing is right will be crucial. You use rail instead of flight in order to save money that adds to the bottom line. Cost accounting is in full swing.
Quick top line growth is more often after acquisitions & mergers, inorganic way to expand. With abundant capital, one could have acquired/merged an existing shop or portal on day1. Inorganic growth is more justified when you have built a foundation and then bring into force newer entities. There is a rise in gross sales figure in addition to adding more employees and suppliers. There are more press coverage and public attention. The deciding factor is whether there is a rise in net profit that justifies the expansion effort. Microeconomic theories like increasing returns to scale find relevance.
Even when one goes for inorganic growth, the business purchased is built organically. So, organic growth and inorganic growth are not mutually exclusive. One strategy could be to go for organic growth in your core business and use inorganic ways to capitalize like a catering firm expanding with acquiring confectionery brands. One could see that more than often the natural way is building a foundation through organic growth and then capitalizing on inorganic growth.
A rough way to look at organic growth and inorganic growth is doing work by yourself equivalent to organic growth and hiring others to do inorganic growth. Acquiring a new business is obviously not hiring in the strict sense.
For a sole proprietor, the choice to grow organically or inorganically is to a great extent about personal preference. For a software vendor, one way could be to acquire newer software brands and other to continue developing the existing product because of bonding that the proprietor has with it irrespective of lost business opportunities. This is one of the reasons why sole proprietorship business remains small and listed companies expand over time, other things remaining constant.