As pointed out, they are certainly not the same, but it might not be a bad idea to track and report on the direct traffic. If there has been outreach done and the company is mentioned in print with a URL, direct traffic (along with some search traffic on the URL or business name itself) is likely to go up. If your email newsletters are not tagged, they're likely to show up under direct traffic. Depending on your role, some of what you do under the greater SEO/inbound marketing role can show up under the direct traffic.
The ideal behind this is not only to achieve more traffic, but obtain more qualifed traffic to your website, traffic that arrives at your website with the purpose of purchasing a product or service. There are many agencies and budgets available, yet at the time when Choosing SEO Services make sure they cater for your needs and strike the right balance between budget and objectives.
Clients turn to search engines because they really need a product or service. They have already created a need; it only remains to find a company that suits their interests. It is a medium that can easily encourage conversion, if the company offers what the customer is looking for; the visit will result in action by the customer, either a direct purchase, request for a quote, or more information for a later purchase.
Search Engine Marketing or SEM encompasses the steps taken to increase relevant traffic to your website, through higher rankings on search engines. Traditional SEM is made up of two processes: “organic” search engine optimization (SEO) and pay-per-click advertising (PPC) (or cost-per-click (CPC)). However, the field of SEM is a changing and expanding field thanks to constant new developments, such as:
The term was first used by Internet theorist John Kilroy in a 2004 article on paid search marketing. Because the distinction is important (and because the word "organic" has many metaphorical uses) the term is now in widespread use within the search engine optimization and web marketing industry. As of July 2009, "organic search" is now common currency outside the specialist web marketing industry, even used frequently by Google (throughout the Google Analytics site, for instance).
Together is better! For many businesses, the best approach is a mix of both organic and paid search results. The advantage of this approach is that organic rankings give a business credibility and evergreen search results. Paid search (PPC) provides immediate top-of-the-page listings and greater click through rates, i.e., sales, when consumers are ready to purchase.
Google claims their users click (organic) search results more often than ads, essentially rebutting the research cited above. A 2012 Google study found that 81% of ad impressions and 66% of ad clicks happen when there is no associated organic search result on the first page. Research has shown that searchers may have a bias against ads, unless the ads are relevant to the searcher's need or intent 
So if you're in the local space and you're saying, "Gosh, Google has really taken away the ability for my website to get the clicks that it used to get from Google local searches," going into Google My Business and optimizing to provide information such that people who perform that query will be satisfied by Google's result, yes, they won't get to your website, but they will still come to your business, because you've optimized the content such that Google is showing, through Google My Business, such that those searchers want to engage with you. I think this sometimes gets lost in the SEO battle. We're trying so hard to earn the click to our site that we're forgetting that a lot of search experience ends right at the SERP itself, and we can optimize there too.