Stellar Lumens could be considered both a Ripple freed from the bank joints and a descendant of this cryptocurrency, given that it originated from Ripple site.
Same as the Ripple cryptocurrency, it uses neither proof-of-work, nor proof-of-stake, but an entirely different mechanism, called Consensus Protocol, specifically Federated Byzantine Agreement. This mechanism provides specific groups of nodes, needed for compliance achieving, when the system or distributed consensus are concerned.
Each not has the right to decide who to trust, therefore it does not have to rely on the same trustworthy participants, to achieve consensus. The main purpose of the site of this cryptocurrency is the conversion between various currencies. For example, when one user sends a certain amount in Yen, the user on the other side gets the amount in Dollars, Euros or even Bitcoins. This cryptocurrency is not mineable, and the maximum number of units is 103,491,574,319.