The SME scheme is for small companies defined as having less than 500 employees and a turnover of less than 100 million euros or gross assets of less than 86 million euros on their balance sheets. Importantly it cannot be used to claim for R&D subcontracted to the claimant company.
The RDEC scheme is for companies too large to qualify for SME scheme.
It may also be claimed by SMEs claiming for R&D subcontracted to them by a large company or by another entity that is not trading, for example a university or for R&D that has been subsidised.