Clients often ask me the difference and I give them a simple answer that normally puts an end to the conversation and their questions, much like the answer shane thomas gave, but less detailed.  Direct is people putting in your url in the top and organic is people searching for you.  Here is an example: If I want to buy a book i type in amazon.com (direct traffic) but if i forgot where to buy a book online i search for "where to buy a book online" which directs me to amazon.com (organic traffic).  When i explain it like this, a light bulb goes off and they understand.  Hope that helps.
Anyone who types in a search query has a specific intent. And they’re expecting the content that they find in the SERPs to satisfy that intent. If you can understand the search intent of your prospective customers, it will transform your marketing in several ways. You’ll be able to predict what keywords your potential customers are likely to use.  It’s easy to start targeting keywords with no structure or strategy. But that’s a mistake.
Search engine marketing’s greatest strength is that it offers advertisers the opportunity to put their ads in front of motivated customers who are ready to buy at the precise moment they’re ready to make a purchase. No other advertising medium can do this, which is why search engine marketing is so effective and such an amazingly powerful way to grow your business.
The piece on generating demand for branded queries rather than just product-based ones is particularly interesting here. It sounds as though it'll be more important than ever to have a strong brand in order to succeed (rather than just having a well-optimized site -- and ideally, having the strategic, technical, and creative sides all working together cohesively). Perhaps it's possible that brand exposure through things like answer boxes can still deliver some value too, even if it's difficult to measure, and CTRs are diminished? 

At the retail level, the two top organic food sales categories, receive significant price premiums over conventionally grown products. ERS also analyzed organic prices for 18 fruits and 19 vegetables using 2005 data on produce purchases, and found that the organic premium as a share of the corresponding conventional price was less than 30 percent for over two-thirds of the items. The premium for only one item—blueberries—exceeded 100 percent. In contrast, in 2006, organic price premiums for a half-gallon container of milk ranged from 60 percent for private-label organic milk above branded conventional milk to 109 percent for branded organic milk above private-label conventional milk. See the ERS report for more on this topic:
Well, yes and no. Sure, you can get hit with an algorithm change or penalty that destroys all your traffic. However, if you have good people who know what they are doing, this is not likely to happen, and if it does, it is easy (in most cases) to get your visits back. Panda and Penguin are another story, but if you get hit by those it is typically not accidental.
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