Understanding what search engine optimisation is isn't made any easier by the vast number of different names that surround the subject; often used in different ways by different commentators and practitioners. Let's see if we can bring some clarity to the subject.
The most common term is probably still
Search Engine Optimisation - SEO
The Americans spell it optimization with a z, whereas in Britain we usually prefer the s spelling. Some people use it as a general catch-all description arguing that as the best known term it should be the one to cover the whole industry. Others use it in a narrower sense to mean only the optimisation of a site for natural (or organic) search listings. Though that should take in a variety of expertise in keyword research, server setup, coding and programming, copywriting, site architecture and link building.
Search Engine Marketing - SEM
Is usually taken to include the narrower definition of SEO (as above) as well as Pay Per Click (PPC) management such as Google Adwords or Overture/Yahoo.
Search Engine Positioning - SEP
This term isn't as common but I have heard it used to mean either of the two earlier terms.
Internet Marketing
Generally this covers a wider range than SEM, including areas such as blogging, email marketing, newsletters, podcasting, RSS, and social networking.
There are other topics beyond this which can be even harder to pin down. Analytics may involve various levels of effort aimed at discovering what traffic is arriving at your site and what it is doing when it gets there. Exactly what is entailed and how accurate the figures will be depends on what traffic data is, or can be made, available.
Conversion optimisation is to do with improving the conversion from visitor to buyer and sometimes attempting to channel users through a site to the point where they are most likely to make a purchase.
Here at SpiderWriting SEO we cover most of these areas with the main exception being PPC management. For anything else please contact us via our web form or call 07855 457749 and we'll be happy to advise on the best strategy for your needs.
But whoever you approach for any of these services make sure you know what it is they undertand the various terms to mean and exactly what they'll do to provide them. If for instance they think SEO is just link building and won't tell you how they get them then my advice is to find a professional with a broader understanding and a more open approach.