For example, Gradius III SA-1 version can be downloaded here. For applying BPS patches, you can use FLIPS or beat. For applying IPS patches, you can use Lunar IPS. The most common patch types are IPS and BPS. That's the main issue you have when using patches, because you will need to download a tool for applying the patch and the original game ROM for applying it. When downloading a patch, you will have to use a tool that knows how to read the patch data and apply it over the original game ROM. But the main reason for using and distributing patches is because since they only include the changes made to the ROM, it will not contain any copyrighted code and thus the patches are immune to any copyright claim, unless if patch itself contains copyrighted data. The reason for that is because patches only contain the changes made to the ROM, making them smaller to distribute specially on big ROMs present on newer consoles like Playstation 1, Nintendo 64 and newer.

It's common when distributing new game enhancements, ROM hacks and specific features people end up releasing in patch format instead of uploading the modified ROM image to the public.

How to play rom hacks after downloading