"capitalism + redistribution of resources by the state", if you prefer. But I fear the American-English battle for the word "socialism" is lost.

While food banks are important, as nearly as I can tell most people aren't relying on private charity alone. (I wasn't able to find a number online, but the numbers I did find were that a boatload of people are relying on SNAP, and a huge fraction of the people on SNAP are also relying on food banks, and that number is roughly comparable to the number of people who visit food banks each year, so the number of people who visit food banks without relying on SNAP must be quite small.)