Schedule E is used to report "passive" income. This income is either rental income you receive because you own rental property, or a royalty payment you receive. Passive income is not subject to the additional self-employment tax, and that's why it's reported on SCH E. Passive income is income that you receive, but don't actually work for and "earn".
SCH C is used to report self-employment business income. This is income that you go out and actually "do" something to earn it. This income is reported on SCH C and in addition to the regular income tax, is also subject to the additional self-employment tax, if that SCH C income is more than $399 for the tax year. The Self-Employment tax is basically the employer's side of your social security and Medicare. It gets credited to the Social Security account of the business owner listed on the SCH C, and nobody else.