What are the core differences between SEO, SEM & SEA?

Let me start with marketing, Marketing is a wider range of activities for a product of service.  Marketing Includes 

a) Research

b) Advertising

c) Sales

d) Customer Relation

e) Customer support and service

So the conclusion is, promoting a product or service through search engine optimization and advertising in search engine results pages is called as search engine marketing.

SEO : Optimization your existing rank and pr organically.

SEM : Marketing in Social Media organically or paid.

SEA : Advertising in Social Media this is only Paid Ads.

>> SEM (search engine marketing) it is referred to every effort made to promote your website, blog, services or products on internet. SEM has many branches such as Affiliate marketing, Link building, SEO, SMM, PPC (Adword or SEA), email marketing and etc.

>> SEO (search engine optimization) is a branch of SEM. SEO is referred to organic search (results just based on quality and relevance but not paid).

>> SEA (search engine advertisement) is a branch of SEM.  SEA is referred to the paid advertisement on websites such as Facebook, Google Adword, PPC and etc. 

SEO is Search Enginer Optimization.

It's a technique used to get your website rank high in natural results in search engines (especially google).

i.e. after you do SEO to your site, your site might appear in first page on google when searching for relevant keywords.

SEM (Search Engine Marketing)

You pay google to place your ad above the natural search results.

i.e. you tell googe:

when someone searches for: "best restaurants" please show my ad. It usually appears as the pink/yellow rectangle above the natural results.

SEA (Search Engine Advertising) is the same as SEM.... but this is the first time i hear this term.

people who work in the industry use SEO and SEM.

SEA and SEM reffer to Same thing Search Engine Marketing or Search Engine Advertising , maybe there is theorical debeat which name is good but in real both are same things 

Search Engine Optimization (SEO) is your effeort to get Organic traffic or in simple word getting better position in Search Result 

Where SEM or SEA is your paid effort to get lead / traffic from Search Engine , Where you are paying for every click you get