1. About purpose:
Ripple. Enables multinational companies and banks to quickly make cost-effective international money transfers and currency conversions, plus access to a range of extras. Ripple is a private blockchain company that provides services to other companies.
Stellar. Allow individuals to perform money transfers and currency conversion more effectively. Stellar itself is a non-profit organization with the goal of opening a global payment system.
2. on how it works:
How Ripple works: Banks and multinational corporations use Ripple to make international payments. This is done by transferring the XRP token through the Ripple network. The end result is liquidity on demand.
How Stellar works: Stellar allows individuals to trade money directly with each other, using Lumens (XLM) as a means and an "anchor" to handle traditional monetary aspects.