What is social marketing? Some questions about it...?

I’m having a hard time understanding what exactly social marketing is. I know that it is a technique used by an organization to address a social cause and which seeks to influence public opinion and behavior so that society, not the organization, benefits.

Here are my questions…
Is this an example: The employees of a large corporation that manufactures and sells say, scientific calculators (or any product other than bikes), volunteer to ride their bikes to work in order to decrease carbon emissions. This information is noted on the company website and given to the local news media.

In my opinion, the action of these employees may influence some members of the public to ride their bikes to work, so society benefits by (small-scale) reduced carbon emissions. Therefore, I think this is social marketing. Am I correct?

In the case above, the corporation does not sell more of its product, but does earn goodwill. So, isn’t the corporation benefiting indirectly? Is an indirect benefit an acceptable result of social marketing?

Here’s another example: This corporation donates its scientific calculators to the local schools. The corporation does not profit financially because it is a donation (I’m ignoring the tax benefit of donations here), but again, earns goodwill. This scenario doesn’t influence behavior but does benefit society (the students). Is this considered social marketing?

One more question:
I’ve seen the term ‘social media marketing’, which refers to companies and/or their employees using social networking, such as blogs, to keep the public informed about their products, interests, citizenship. Are social marketing and social media marketing the same?

Thanks!