Yes, there is more. For really color-critical applications, things like the viewing environment are important. There is a way to automatically adjust for that too, using a Color Management System (CMS) which is increasingly being supplied with modern computer systems.
PNG has the capability to contain additional information to take it to this highest quality level. The sRGB color space can be used for accurate, calibrated color with any CMS which understands International Color Consortium (ICC) profiles.
Because this is a well-known profile, it is not necessary to physically embed it in each image created in conformance with sRGB. Which is just as well, since the information takes up around 2000 bytes. Instead, the PNG file just has a small extension chunk added which indicatess the image is in sRGB. This only adds a dozen or so bytes to the image. Because PNG is extensible, this doesn't stop older browsers and image tools - which don't understand sRGB yet - from displaying the image. But newer tools are given the information they need to give even higher quality display.