Well, they are both part of the Theridiidae family. Black widows being part of the Latrodectinae genera, whereas the one up top is from Parasteatoda.
It's a big family. You'll see tons of these all over the world. Basically if it makes a cobweb, it's part of that same family.
Nothing to worry about though. They're great for pest control. The one up top is even known as the common house spider. You probably have some living in your walls right now! And if you didn't, you'd suddenly notice a lot of pests running around instead. They have a great temperament, and aren't likely to bite at all. In fact, it's been noted that you literally have to squeeze them just to get them to bite you as they are so docile.