PNG files are a type of graphic file. JPG (also called JPEG) is the most popular format of a graphic file. GIF files were very popular for simple graphics in a file.
JPG files (Joint Photographic Experts Group) work great for pictures and those type graphics. However they are compressed so each time you open and edit and save them you lose quality like making copies from copies on a copier. The best thing to do is keep the original file unedited and save the edited files to a different name so you can go back to the original file for future editing.
GIF files (graphics interchange format) were popular for doing graphics like logos etc but are low resolution files and do not give ability to have items adjust in color or darkness easily. A major problem with GIF is that it is a format that is owned by an organization (UNISYS) and must be incensed.
PNG files (portable network graphics) were created to be the same type graphics as in a GIF file but at a higher resolution. They were intended for use on the Internet but are use in other places for graphics files also. They are a higher resolution but are non-compressed so will be larger files but are raster vector based which means instead of keeping track of information dot by dot as in JPG, they keep as math coordinates like in a graph of where information goes which reduces the size and also gets rid of the problem of quality declining when you edit and edited file. PNG will not work well for images like pictured but works well for images like logos.
Unless you are doing graphics designing of some type you may never work with PNG and GIF files. If you have seen where people can earn badges on the Internet (or have earned any) these are usually done as PNG files. Your pictures are normally done as JPG although could be RAW or TIF.