Let's establish terminology first. SEO stands for Search Engine Optimisation and SEM stands for Search Engine Marketing.
Now, the basics. SEM refers to a broad range of processes including paid placements, paid inclusions and SEO itself, while SEO relies on searching content for keywords (organic is the usual term applied to SEO). SEO is a process while SEM is a collective term for a group of processes. Put simply, SEO, although it can function alone, is one part of SEM. Again, keeping it simple, the three most important differences from a marketing standpoint are:
1) SEO is cheaper.
Much cheaper in fact. SEO uses a site's content to give it a rank in search engines largely based on keywords. A type of search engine software called a spider is used to index your site's content, when a person enters keywords for a search this index is used to rank your site by relevance based on a person's search criteria. SEM involves more direct marketing and some elements of it cost money. Paid inclusion for example involves paying a search engine company to be included on their search lists.
2) SEO is more important.
That's a generalization (especially since SEO is part of SEM) and from a marketing standpoint there is definitely an argument that SEM is more important. Perhaps a better way of putting it would be to say that SEO comes first. Bottom line, if your site does not contain the keywords necessary for a person to find it organically, then it is not going to be a useful site to them, and even if they find it, they will not use it. SEO relies on content, and although SEM will get people to your site, if the content is not there, then getting them to your site was pretty pointless. In other words, content comes first!
3) SEM is faster.
Much faster, in fact. It takes time for the search engine spiders to go through the content of your site and index it so that your site can be found via SEO alone. In fact, it could be months before this approach pays off. So, either you have to plan a great deal in advance or you need SEM as well. SEM, once it is in place, will give you instant results. (But remember that content still has to be in place, there is no point in paying for customers to be directed to a useless site.)