Why do stars sometimes look like blobs or distorted shapes in photos?

That's a combination of defocus and distortion, most commonly caused by "seeing" -- the astronomical term for the refractive conditions of the air column between the lens and the star.

A star is effectively a point source, but air movement and density variations (similar to the ripples over a metal roof on a hot day) can momentarily distort the image. This is why classical star photographs (made with long exposures and a tracking telescope) show brighter stars as larger -- because they can adequately expose a larger area of film as the "seeing" makes the star image dance around.

Take a short exposure, however, and you can wind up with this, a momentary capture of the distorted image, without the time averaging that would come from exposing film for an hour or more.

Use a laser as an "artificial star" and take a bunch of these images in rapid succession, record them in a way to preserves the phase of the light, and then let a well programmed computer work on the data for a while, and you can do what's called "speckle interferometry" -- which was used to make the first images of stars (other than our own Sun) as a disk. Record a conventional video, however, and you may be able to pick up the clearest frames and add or average them to get much clearer images than the overall seeing would permit -- this is called "stacking" and is used to, among other things, record images at higher resolution than the actual sensor pixel size.