I will try my best to explain these terms since I know from personal experience how confusing they can be at the beginning.
SEO = search engine optimization
SEM = search engine marketing
SMO = social media optimization
SMM = social media marketing
Now that you understand what each acronym means you probably also understand what it focuses on.
SEO and SEM revolve around search engine. They are fairly similar but SEM usually involves paying for the ads such as PPC and CPC. SEO is all about trying to get your website/blog/product to rank the highest possible when somebody looks for it through the search engine. If I look for "coffee" you want your coffee website to come out on first page on the search engine.
SMO and SMM revolve around social media (Facebook, Twitter, ...).
SMO basically focuses on increasing the visibility of your social media sites and profiles. As a result you can draw more traffic to your blogs, websites, and so on.
For SMM it is typical to pay for such advertisement. Facebook ads can be a good example.
Hope this helps. If any further questions just ask away