Photos have lots of noise anyway, so a good jpeg is not going to be the limiting factor. Due to jpeg being lossy, the file size is much smaller for the type of images that pictures are (I don't know a formal definition, perhaps something with some amount of random noise? Or that there's lots of gradients with nonlinear slopes or so?).
PNGs are lossless, and encoding photos in a lossless way takes a relatively large amount of space. On the other hand, the quality degradation of running text through a jpeg encoder is noticeable even when tuning the jpeg compressor for it, so a screenshot with text is always PNG. For designed things such as icons or logos or so, the file size is small enough to be a no-brainer for getting PNG's lossless quality.
Vector, such as SVG, is the ultimate format: the highest possible quality and also the smallest! This only works when you've got access to the source (screenshots already don't work because you're capturing a blend of objects rendered as an array of pixels), and especially not suitable/possible when you're reading from a sensor such as a digital camera. This format doesn't describe pixel patterns, but rather shapes such as "draw a red line from coordinates 3,94 to 1920,1027". Because you can't always use it (you can always render an SVG as a grid of pixels and turn it into a PNG or anything else, but not the other way around), support is a bit lower and you'll see them less often, but imo it's always worth striving for when the platform allows
