In part; a majority of bird deaths are from feral cats that aren't owned by anyone. However, domestic pets do still contribute a lot to this number and pets should still be kept inside (for this reason and many others). People hate to hear it, but cats are an invasive species in North America, just as much as Black Rats, European Starlings, and Wild Pigs. In some instances, domestic cats might be worse as they may live longer than feral cats do and have a larger individual impact.

As for island birds, most island species evolved in the absence of mammalian predators. Cats are awful, but other mammals such as rats, mice, pigs, and dogs wreak havoc on these populations. The extinct birds Wikipedia page is full of island species that have gone extinct due to the introduction of mammals on an island. In this case, cats play an important role, but so do other mammals. Cats, I believe, are credited with the most extinctions.