SEO and SEM are two very different actions although both fit within the category of Internet Branding or Net Branding.
SEO involves actions such as link building, social media marketing and article marketing that really should not cost you much other than for the services of a professional in this area whether this be a PR / writer to create well written content for your organisation to release or for a Social Media Professional to conduct the SEO on your behalf. SEO requires a time commitment to achieve results.
On the other hand SEM or Search Engine Marketing typically involves paid marketing. This includes Pay Per Click (PPC) marketing and usually delivers faster results in the short term allowing you to build up your SEO over the medium to longer term.
A conscious decision aligning your social media objectives to your planned actions / available budget will assist in making the decision as to whether SEO or SEM will be better suited to your organisation.