How are the Stellar Consensus Protocol and the XRP Ledger Consensus Process different, and what does it mean for users?
Tl;dr: Stellar’s protocol (SCP) uses a decentralized state propagation where each node commits to a value if every node it deems trustworthy agrees while Ripple uses a supermajority vote (80%) among all validating nodes. Stellar achieves better decentralization than Ripple.
Stellar started out as a fork of Ripple (now completely rewritten) so they are pretty similar in implementation and use cases.
Stellar uses the Stellar Consensus Protocol (SCP) to achieve decentralization, while Ripple uses the XRP Ledger Consensus Process. These are alternatives to Bitcoin's proof of work whose goal is to have every participant in the network agree on the current state.
In SCP, each node decides for itself which other nodes it trusts. When a lot of these sets of trusted nodes are overlapping, there is a high probability there is agreement on the state of the network. Broadly, a node will only accept a message if all of their trustworthy nodes have in turn accepted it. This is similar to the way internet certificates and DNS servers are working. In principle, there is no central authority appointing trustworthy nodes, but de facto, the network will reach an agreement on which nodes are trustworthy. This is a great video explaining SCP in detail. There is also the white paper for more formal mathematical definitions.
Ripple on the other hand uses a set of special nodes called "validating nodes". A new state is transmitted to all validating nodes and whenever 80% of them agree on it, the ledger is updated. Anyone can launch a validating node, but Ripple recommends they register and disclose their identity. In principle, this model doesn't make Ripple less decentralized than Stellar. However, in practice, the company Ripple controls most validating nodes, as there is no incentive for anyone to run these nodes (transaction fees are destroyed). You can see a list of validating nodes here: https://xrpcharts.ripple.com/#/validators
Another difference is that Ripple is a deflationary currency (a certain amount of XRP is destroyed at each transaction to prevent spamming the network), while Stellar is inflationary. This doesn't necessarily mean that Ripple is a better store of value, since all inflation is returned to Stellar users through inflation pools.
Other than the technology, it is important to mention differences between development philosophies that are driving the two projects: XRP is developed by a for-profit company (Ripple) while Stellar is developed by the Stellar Development Foundation which is a non-profit. Stellar places a greater emphasis on serving the underbanked and facilitating payments between individuals across borders, while Ripple is mainly focused on financial institutions.