What a GIF file actually is
GIF dates to 1987 and stores at most 256 colours from a palette, compressed losslessly with LZW. Transparency is a single on/off flag on one palette entry rather than a real alpha channel, which is why GIF edges against a coloured background look jagged.
GIFs come from the reaction-image corner of the internet, from old web assets, and from screen recorders that default to it. Anything animated and low-colour that has been passed around for years is probably still a GIF.
What you get from PNG
PNG output is lossless, so the saved pixels are exactly the pixels that went in and re-saving costs nothing in quality. It keeps a full 8-bit alpha channel, which means soft shadows and anti-aliased edges survive against any background.
Universal since the early 2000s, and the format every design tool, browser and operating system handles without argument. It is also the safest format to hand to a printer or a colleague when you do not know their software.
What changes when you convert GIF to PNG
Both formats are lossless, so nothing is thrown away in either direction — this is a container change rather than a quality decision. What differs is how efficiently each one packs the same pixels, and how widely each is supported by the software you need to open it in.
Transparency technically survives, but it improves on the way. GIF has no alpha channel — just one palette entry flagged as transparent — which is why GIF cut-outs have hard, jagged edges. PNG stores a full 8-bit alpha, so anything you composite afterwards can have genuinely smooth edges, even though the original's jaggedness is baked in.
Only the first frame survives. GIF is the one source here that can be animated, and PNG output is a still image, so an animated GIF converts to its opening frame. The upside for static GIFs is real: escaping the 256-colour palette removes the banding, and the file usually gets smaller at the same time.