The previous post-er is correct on all counts, but I'd add a couple of things that will shed light on 'shareholder':
Depending on the firm, there are usually a few shades of Partner. Associates are usually elevated to Partner based on two things: 1) experience in practicing law and 2) development of a "book of business," i.e. going out and getting their own clients.
Whether you're named a Partner or an Equity Partner/Shareholder depends on the the age and size of the firm, your performance, etc. Both designations get a share of the profits, but equity/s.h. reinvest some of this money into the partnership annually. Their stake is akin to stock in a company...at some point, they can cash out their share of the partnership.