SEO + SEA + SMO = SEM... confused then solution is hear

I will begin this post the straw that broke the camel's the story that inspired me to write a few weeks ago a colleague (I salute if it recognizes and to whom I have absolutely no criticism) contacted me quickly via phone one of our wholesale accounts for which we manage the channel "email marketing" needed a SEM analysis urgent and had a budget of over a hundred thousand. 
So I made ​​a complete study in SEO and SEA for the client before sending it to my colleague who was surprised to see the presentation in two parts: 1) SEO 2) SEA ... She expected to see the study focused on an SEA analysis since for her and Unfortunately for many, SEM = SEA ... Even today she asks me how is the SEM whereas it only works on Adwords campaign for this client!

I almost feel compelled to write an article to put some order in the world of 3-letter acronyms of search-marketing  !

Start with the basics and define the different acronyms:

• SEO (search engine optimization) : natural SEO in French, ref nat, organic or owner is linked to the position of your site in search engine activity.
• SEA (search engine advertising or PPC, CPC): do not confuse sponsored links (purchase space and keywords on search engines like Google Adwords) and paid search (pay services to register in directories, engines, comparators). 
  PARS is to position its site in the search engine return for payment.
• SMO (social media optimization) : optimization in French on social networks. This is to give more visibility to a di site from social networks such as Facebook, Twitter, Youtube, Dailymotion, Digg ... Not to be confused with the SMM is the working relationship between the company and the community on social networks .
• SEM (SM, search engine marketing or search engine marketing) : French in SEO or "search." This means all activities related to SEO your website on the SERPs. 
  So to summarize SEM = SEO + SEA + SMO .

Why this rant?

I increasingly feel that many people use the acronym SEM all the sauces to say everything and anything and that the more time passes the phenomenon is spreading ... 
How many times have I heard say, "we do SEO and SEM" and then "we want to make a SEM campaign Adwords" ...

But I want to reassure my colleague ( see story ), it's not necessarily his fault ... For example, type in your favorite "engine definition SEM . " Wikipedia great location gives us a definition does not even mention once the SEO:

But am I right? All these people makes me doubt by repeating the &% $ #!

Let's be rational in SEM ago Marketing right? So I ask you (rétoriquement) if the SEO is not a marketing activity? And why we should put aside?

SEM = SEO + SEA + SMO , we all agree now? 
The pointillist tell me that my equation is incomplete and could be added to the formula local SEO, videos, images, products that can be displayed on the SERP ... I want to say yes but ...